Malliavin-Stein approach
A webpage maintained by Ivan Nourdin

#### Why this webpage?

• In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the ``fourth moment theorem'' in the sequel; alternative proofs can be found here, here and here) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is actually equivalent to convergence of just the fourth moment! Shortly afterwards, Peccati and Tudor gave a multidimensional version of this characterization.

• Since the publication of these two pathbreaking papers, many improvements and developments on this theme have been considered. Among them is the work by Nualart and Ortiz-Latorre, giving a new proof only based on Malliavin calculus and the use of integration by parts on Wiener space. A second step is my joint paper ``Stein's method on Wiener chaos" written in collaboration with Peccati in which, by bringing together Stein's method with Malliavin calculus, we were able (among other things) to associate quantitative bounds to the fourth moment theorem.

• It turns out that Stein's method and Malliavin calculus fit together admirably well, and that their interaction has led to some remarkable new results involving central and non-central limit theorems for functionals of infinite-dimensional Gaussian fields.

• This webpage aims to gather all the available resources research papers having any link with the fourth moment theorem and related stuff. I have tried to be as comprehensive as possible, but several links are surely missing. In case, please feel free to contact me (inourdin@gmail.com).

#### Year 2020

1. H. Araya and C.A. Tudor (2020): Asymptotic expansion for the quadratic variations of the solution to the heat equation with additive white noise, Stoch. Dynamics

2. O. Assaad and C.A. Tudor (2020): Parameter identification for the Hermite Ornstein–Uhlenbeck process, Stat. Inference Stoch. Process

3. O. Assaad, D. Nualart, C.A. Tudor and L. Viitasaari (2020): Quantitative normal approximations for the stochastic fractional heat equation

4. J.-M. Azaïs, F. Dalmao and J.R. León (2020): Studying the winding number of a Gaussian process: the real method

5. E. Azmoodeh, M.M. Ljungdahl and C. Thäle (2020): Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages

6. E. Azmoodeh, Y. Mishura and F. Sabzikar (2020): How does tempering affect the local and globalproperties of fractional Brownian motion?

7. M. F. Balde, R. Belfadli and K. Es-Sebaiy (2020): Berry-Esséen bound for drift estimation of fractional Ornstein-Uhlenbeck process of second kind

8. R. Belfadli, K. Es-Sebaiy and F.-E. Farah (2020): Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean

9. S. Bourguin, C.-P. Diez and C.A. Tudor (2020): Limiting behavior of large correlated Wishart matrices with chaotic entries

10. S. Bourguin, S. Gailus and K. Spiliopoulos (2020): Discrete-time inference for slow-fast systems driven by fractional Brownian motion

11. C. Chen, J. Cui, J. Hong and D. Sheng (2020): Convergence of Density Approximations for Stochastic Heat Equation

12. L. Chen, D. Khoshnevisan, D. Nualart and F. Pu (2020): Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition

13. L. Chen, D. Khoshnevisan, D. Nualart and F. Pu (2020): Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method

14. Y. Chen and H. Zhou (2020): Parameter estimation for an Ornstein-Uhlenbeck Process driven by a general Gaussian noise

15. R. Chertovskih and E. Shamarova (2020): Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression

16. I. Cialenco and H.-J. Kim (2020): Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise revised

17. M. Diaz, A. Jaramillo and J.C. Pardo (2020): Fluctuations for matrix-valued Gaussian processes

18. K. Es-Sebaiy and J. Moustaaid (2020): Optimal Berry-Esséen bound for Maximum likelihood estimation of the drift parameter in α-Brownian bridge

19. X. Fang, Y. Koike (2020): High-dimensional Central Limit Theorems by Stein's Method

20. V. Garino, I. Nourdin, D. Nualart and M. Salamat (2020): Limit theorems for integral functionals of Hermite-driven processes

21. J. Gehringer and X.-M. Li (2020): Functional limit theorems for the fractional Ornstein-Uhlenbeck process

22. J. J. Grygierek (2020): Random Geometric Structures, PhD thesis, Universität Osnabrück

23. R. B. Guerrero, D. Nualart and G. Zheng (2020): Averaging 2d stochastic wave equation

24. H. Jiang, H. Liu and Y. Zhou (2020): Asymptotic properties for the parameter estimation in Ornstein-Uhlenbeck process with discrete observations, Electron. J. Statistics 14, pp. 3192-3229

25. D. Lygkonis and N. Zygouras (2020): Edwards-Wilkinson fluctuations for the directed polymer in the full L2-regime for dimensions d≥3

26. D. Khosnevisan, D. Nualart and F. Pu (2020): Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension d≥1

27. C. Macci, M. Rossi and A.P. Todino (2020): Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics

28. D. Marinucci, M. Rossi and A. Vidotto (2020): Non-Universal Fluctuations of the Empirical Measure for Isotropic Stationary Fields on S2 x R

29. D. Mikulincer (2020): A CLT in Stein's distance for generalized Wishart matrices and higher order tensors

30. M. Notarnicola (2020): Fluctuations of nodal sets on the 3-torus and general cancellation phenomena

31. I. Nourdin, G. Peccati and X. Yang (2020): Multivariate normal approximation on the Wiener space: new bounds in the convex distance

32. D. Nualart and G. Zheng (2020): Central limit theorems for stochastic wave equations in dimensions one and two

33. N. Privault and G. Serafin (2020): Normal approximation for generalized U-statistics and weighted random graphs

34. Q. Yu (2020): symptotic properties for q-th chaotic component of derivative of self-intersection local time of fractional Brownian motion, J. Math. Anal. Appl., in press

#### Year 2019

1. F. Alazemi, S. Douissi and Kh. Es-Sebaiy (2019): Berry–Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process with discrete observations, Теория вероятн. и ее примен. 64, no. 3, pp. 502–525

2. F. Alazemi, S. Douissi and Kh. Es-Sebaiy (2019): Berry-Esseen bounds for drift parameter estimation of discretely observed fractional Vasicek-type processes, Theory of Stochastic Processes 40, no. 1, pp. 6-18

3. E. Azmoodeh, P. Eichelsbacher and L. Knichel (2019): Optimal Gamma Approximation on Wiener Space

4. A. Basse-O'Connor, M. Podolskij and C. Thäle(2019): A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages

5. D. Bell, R. Bolanos and D. Nualart (2019): Limit theorems for singular Skorohod integrals

6. S. Bourguin and S. Campese (2019): Approximation of Hilbert-valued Gaussian measures on Dirichlet structures

7. V. Cammarota and D. Marinucci (2019): On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics

8. A. Caponera and D. Marinucci (2019): Asymptotics for Spherical Functional Autoregressions

9. Y. Chen and Y. Liu (2019): Complex Wiener-Itô Chaos Decomposition Revisited

10. I. Cialenco, F. Delgado-Vences and H.-J. Kim (2019): Drift Estimation for Discretely Sampled SPDEs

11. F. Dalmao, A. Estrade and J. León (2019): On 3-dimensional Berry's model

12. S. Douissi, K. Es-Sebaiy, F. Alshahrani and F. Viens (2019): AR(1) processes driven by second-chaos white noise: Berry-Esséen bounds for quadratic variation and parameter estimation

13. M. Duerinckx (2019): On the size of chaos via Glauber calculus in the classical mean-field dynamics

14. N. T. Dung, T. C. Son, T. M. Cuong, N. V. Tan and T. N. Quynh (2019): Density Estimates for Solutions of Stochastic Functional Differential Equations, Acta Mathematica Scientia 39, no. 4, pp. 955-970

15. N. Fountoulakis and J. Yukich (2019): Limit theory for the number of isolated and extreme points in hyperbolic random geometric graphs

16. J. Grygierek (2019): Multivariate Normal Approximation for functionals of random polytopes

17. R. Herry (2019): Stable limit theorems on the Poisson space

18. J. Huang, D. Nualart, L. Viitasaari and G. Zheng (2019): Gaussian fluctuations for the stochastic heat equation with colored noise

19. Z.M. Khalil and C.A. Tudor (2019): Estimation of the drift parameter for the fractional stochastic heat equation via power variation, Modern Stochastics: Theory and Applications 6, no. 4, pp. 397--417

20. Y.T. Kim and H.S. Park (2019): The optimal third moment theorem, J. Korean Statist. Soc., to appear

21. L. Knichel (2019): Fine Asymptotics for Models with Gamma Type Moments and Rates of Convergence on Wiener Space, PhD thesis

22. Y. Koike (2019): High-dimensional central limit theorems for homogeneous sums

23. S. Kuzgun and D. Nualart (2019): Rate of Convergence in the Breuer-Major Theorem via Chaos Expansions

24. I. Nourdin, D. Nualart and G. Peccati (2019): The Breuer-Major Theorem in total variation: improved rates under minimal regularity

25. D. Nualart (2019): Malliavin Calculus and Normal Approximations

26. D. Nualart and A. Tilva (2019): Continuous Breuer-Major theorem for vector valued fields

27. D. Nualart and G. Zheng (2019): Oscillatory Breuer-Major theorem with application to the random corrector problem

28. D. Nualart and G. Zheng (2019): Averaging Gaussian functionals

29. G. Peccati and A. Vidotto (2019): Gaussian Random Measures Generated by Berry's Nodal Sets

30. R. Shevchenko, M. Slaoui and C.A. Tudor (2019): Generalized k-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus

31. M. Slaoui and C.A. Tudor (2019): Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index

32. M. Slaoui and C.A. Tudor (2019): Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs

33. G.-L. Torrisi, E. Leonardi (2019): Almost Sure Central Limit Theorems in Stochastic Geometry

34. C.A. Tudor and N. Yoshida (2019): High order asymptotic expansion for Wiener functionals

35. L. Viitasaari (2019): Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences, Probab. Surveys 16, pp. 62-98

36. M. Zili and E. Zougar (2019): Spatial quadratic variations for the solution to a stochastic partial differential equation with elliptic divergence form operator, Modern Stochastics: Theory and Applications (2019), pp. 1-31

37. N. Zygouras (2019): The 2D KPZ as a marginally relevant disordered system

38. N. Zygouras (2019): Discrete stochastic analysis

#### Year 2018

1. H. Araya and C.A. Tudor (2018): Behavior of the Hermite sheet with respect to the Hurst index, Stoch. Proc. Appl., in press

2. D. Armentano, J.-M. Azaïs, F. Dalmao and José León (2018): Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems

3. J.-M. Azaïs, D. Armentano, F. Dalmao and José León (2018): Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems

4. E. Azmoodeh, P. Eichelsbacher and L. Knichel (2018): On the Rate of Convergence to a Gamma Distribution on Wiener Space

5. E. Azmoodeh and D. Gasbarra (2018): On a new Sheffer class of polynomials related to normal product distribution

6. E. Azmoodeh and I. Nourdin (2018): Almost sure limit theorems on Wiener chaos: the non-central case

7. E. Azmoodeh and G. Peccati (2018): Malliavin-Stein Method: a Survey of Recent Developments

8. C. Berzin (2018): Estimation of Local Anisotropy Based on Level Sets

9. S. Bourguin, S. Campese, N. Leonenko and M. S. Taqqu (2018): Four moments theorems on Markov chaos

10. V. Cammarotta and D. Marinucci (2018): A Reduction Principle for the Critical Values of Random Spherical Harmonics

11. S. Campese, I. Nourdin and D. Nualart (2018): Continuous Breuer-Major theorem: tightness and non-stationarity

12. Y. Chen, N. Kuang and Y. Li (2018): Berry-Esseen bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes

13. G. Cébron (2018): A quantitative fourth moment theorem in free probability theory

14. T. Courtade (2018): Bounds on the Poincaré constant for convolution measures

15. F. Delgado-Vences, D. Nualart and G. Zheng (2018): A Central Limit Theorem for the stochastic wave equation with fractional noise

16. C. Döbler and G. Peccati (2018): Limit theorems for symmetric U-statistics using contractions

17. C. Döbler and G. Peccati (2018): Fourth moment theorems on the Poisson space: analytic statements via product formulae

18. A. Dunlap, Y. Gu, L. Ryzhik and O. Zeitouni (2018): Fluctuations of the solutions to the KPZ equation in dimensions three and higher

19. M. Fathi (2018): Stein kernels and moment maps

20. Y. Gu (2018): Gaussian fluctuations of the 2D KPZ equation

21. J. Hazla, E. Mossel, N. Ross and G. Zheng (2018): The Probability of Intransitivity in Dice and Close Elections

22. J. Huang, D. Nualart and L. Viitasaari (2018): A Central Limit Theorem for the stochastic heat equation

23. M. Khalil and C.A Tudor (2018): Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise, Electron. J. Statist. 12, number 2, pp. 3639-3672.

24. P. Kriz and B. Maslowski (2018): Central Limit Theorems and Minimum-Contrast Estimators for Linear Stochastic Evolution Equations

25. G. Last, F. Nestmann and M. Schulte (2018): The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation

26. N. Ma and D. Nualart (2018): Rate of convergence for the weighted Hermite variations of the fractional Brownian motion

27. D. Müller (2018): Central Limit Theorems for Geometric Functionals of Gaussian Excursion Sets, PhD thesis, Karlsruher Institut für Technologie

28. I. Nourdin and D. Nualart (2018): The functional Breuer-Major theorem

29. I. Nourdin, G. Peccati and X. Yang (2018): Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality

30. I. Nourdin and G. Zheng (2018): Asymptotic behavior of large Gaussian correlated Wishart matrices

31. D. Nualart and H. Zhou (2018): Total variation estimates in the Breuer-Major theorem

32. N. Privault (2018): Third Cumulant Stein Approximation for Poisson Stochastic Integrals, J. Theoret. Probab., to appear

33. N. Privault and G. Serafin (2018): Normal approximation for sums of discrete U-statistics - application to Kolmogorov bounds in random subgraph counting

34. N. Privault, S.C.P. Yam and Z. Zhang (2018): Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates, Stoch. Proc. Appl., to appear

35. M. Rossi (2018): Random Nodal Lengths and Wiener Chaos, Proceedings of the Workshop "Probabilistic Methods in Spectral Geometry and PDE", CRM Montreal - August 2016

36. M. Schulte and J.E. Yukich (2018): Multivariate second order Poincaré inequalities for Poisson functionals

37. M. Slaoui and C.A. Tudor (2018): Limit behavior of the Rosenblatt Ornstein–Uhlenbeck process with respect to the Hurst index, Theory Probab. Math. Statist. 98, pp. 173-187

38. A. P. Todino (2018): Nodal Lengths in Shrinking Domains for Random Eigenfunctions on S2

39. D. Tran (2018): Contributions to the asymptotic study of Hermite driven processes, PhD thesis, University of Luxembourg

40. G. Zheng (2018): Recent developments around the Malliavin-Stein approach – Fourth moment phenomena via exchangeable pairs, PhD thesis, University of Luxembourg

#### Year 2017

1. B. Arras, E. Azmoodeh, G. Poly and Y. Swan (2017): A bound on the 2-Wasserstein distance between linear combinations of independent random variables

2. B. Arras, E. Azmoodeh, G. Poly and Y. Swan (2017): Stein characterizations for linear combinations of gamma random variables

3. E. Azmoodeh and D. Gasbarra (2017): New moments criteria for convergence towards normal product/tetilla laws

4. D. Bell and D. Nualart (2017): Noncentral limit theorem for the generalized Rosenblatt process

5. S. Bourguin and S. Campese (2017): Free quantitative fourth moment theorems on Wigner space

6. S. Bourguin and I. Nourdin (2017): Freeness characterizations on free chaos spaces

7. V. Cammarota (2017): Nodal area distribution for arithmetic random waves

8. Y. Chen, Y. Hu and Z. Wang (2017): Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise

9. Y. Chen and G. Jiang (2017): A note on the Moment of Complex Wiener-Ito Integrals

10. C. Döbler and K. Krokowski (2017): On the fourth moment condition for Rademacher chaos

11. C. Döbler and G. Peccati (2017): The fourth moment theorem on the Poisson space

12. C. Döbler, A. Vidotto and G. Zheng (2017): Fourth moment theorems on the Poisson space in any dimension

13. S. Douissi, K. Es-Sebaiy and F.G. Viens (2017): Berry-Esséen bounds for parameter estimation of general Gaussian processes

14. T. Fissler (2017): On Higher Order Elicitability and Some Limit Theorems on the Poisson and Wiener Space, PhD thesis, University of Bern

15. M. Gao and J. Fang (2017): Multidimensional Free Poisson Limits on Free Stochastic Integral Algebras

16. A. Granelli and A. Veraart (2017): A central limit theorem for the realised covariation of a bivariate Brownian semistationary process

17. D. Harnett, A. Jaramillo and D. Nualart (2017): Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes

18. Y. Hu, D. Nualart and H. Zhou (2017): Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter

19. P. V. Hung (2017): Quantitative Central Limit Theorems of Spherical Sojourn Times of Isotropic Gaussian Fields, Acta Math Vietnam

20. A. Jaramillo and D. Nualart (2017): Functional limit theorem for the self-intersection local time of the fractional Brownian motion

21. M. Khalil, C.A. Tudor and M. Zili (2017): Spatial variation for the solution to the stochastic linear wave equation driven by additive space-time white noise, Stoch. Dyn., in press

22. Y. Kim and H. Park (2017): Optimal Berry–Esseen bound for statistical estimations and its application to SPDE, J. Multi. Anal., in press

23. Y. Kim and H. Park (2017): Optimal Berry–Esseen bound for an estimator of parameter in the Ornstein–Uhlenbeck process, J. Korean. Statist. Society, in press

24. Y. Kim and H. Park (2017): Convergence rate of a test statistics observed by the longitudinal data with long memory, Comm. Stat. Appl. Methods 24, pp. 481-492

25. M. Kratz and S. Vadlamani (2017): Central Limit Theorem for Lipschitz–Killing Curvatures of Excursion Sets of Gaussian Random Fields, J. Theoret. Probab., in press

26. K. Krokowski and C. Thaele (2017): Multivariate central limit theorems for Rademacher functionals with applications

27. R. Lachièze-Rey, M. Schulte and J.E. Yukich (2017): Normal approximation for stabilizing functionals

28. D. Marinucci, M. Rossi and I. Wigman (2017): The Asymptotic Equivalence of the Sample Trispectrum and the Nodal Length for Random Spherical Harmonics

29. I. Nourdin, G. Peccati and M. Rossi (2017): Nodal Statistics of Planar Random Waves

30. I. Nourdin and D. Tran (2017): Statistical inference for Vasicek-type model driven by Hermite processess

31. I. Nourdin and G. Zheng (2017): Exchangeable pairs on Wiener chaos

32. D. Novotna and V. Benes (2017): Central limit theorem for functionals of Gibbs particle processes

33. R. Passeggeri and A. Veraart (2017): Limit theorems for multivariate Brownian semistationary processes and feasible results

34. G. Peccati and M. Rossi (2017): Quantitative limit theorems for local functionals of arithmetic random waves

35. N. Privault and G. Serafin (2017): Stein approximation for functionals of independent random sequences

36. N. Privault and Q. She (2017): Conditional Stein approximation for Itô and Skorohod integrals, Stat. Probab. Letters, in press

37. X. Sun and L. Yan (2017): Central limit theorems and parameter estimation associated with a weighted-fractional Brownian motion, J. Statist. Plan. Inf., in press

38. C. Thaele, N. Turchi and F. Wespi (2017): Random polytopes: variances and central limit theorems for intrinsic volumes

39. C. Tudor, N. Yoshida (2017): Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

40. N. Turchi and F. Wespi (2017): Limit theorems for random polytopes with vertices on convex surfaces

41. J. Viquez (2017): Normal Convergence Using Malliavin Calculus With Applications and Examples, Stochastic Analysis and Applications 2017

42. G. Zheng (2017): A Peccati-Tudor type theorem for Rademacher chaoses

#### Year 2016

1. S. Bai (2016): Probabilistic and statistical problems related to long-range dependence, PhD thesis, Boston University

2. B. Bhattacharya, P. Diaconis and S. Mukherjee (2016): Universal Limit Theorems in Graph Coloring Problems With Connections to Extremal Combinatorics, Ann. Appl. Probab., to appear

3. G. Binotto, I. Nourdin and D. Nualart (2016): Weak symmetric integrals with respect to the fractional Brownian motion

4. S. Bourguin and C. Durastanti (2016): On normal approximations for the two-sample problem on multidimensional tori

5. S. Bourguin and C. Durastanti (2016): On high-frequency limits of U-statistics in Besov spaces over compact manifolds

6. V. Cammarota and D. Marinucci (2016): A Quantitative Central Limit Theorem for the Euler-Poincaré Characteristic of Random Spherical Eigenfunctions

7. F. Caravenna, R. Sun and N. Zygouras (2016): Scaling limits of disordered systems and disorder relevance

8. L. Chen (2016):  A Diffusion Model for Compositional Data, PhD thesis, Kent State University

9. L. H. Y. Chen, Y.-J. Lee and H.-H. Shih (2016):  Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus

10. C. Döbler and G. Peccati (2016): Quantitative de Jong theorems in any dimension

11. C. Döbler and G. Peccati (2016): The Gamma Stein equation and non-central de Jong theorems

12. K. Es-Sebaiy and F. Viens (2016): Optimal rates for parameter estimation of stationary Gaussian processes

13. M. Fathi and B. Nelson (2016): Free Stein kernels and an improvement of the free logarithmic Sobolev inequality

14. T. Fissler and C. Thaele (2016): A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes

15. A. Gouwy (2016): On various aspects of Stein's method: quantitative approximation for stochastic limit theorems, Master thesis, Universiteit Gent

16. J. Grygierek and C. Thaele (2016): Gaussian fluctuations for edge counts in high-dimensional random geometric graphs

17. Y. Kim and H. Park (2016): Berry–Esseen Type bound of a sequence Xn/Yn and its application, J. Korean Statist. Soc., in press

18. R. Malukas (2016): A Berry–Esséen bound for H-variation of a Gaussian process, Lithuanian Mathematical Journal 56, no. 1, pp. 77-106

19. T. Mastrolia (2016): Density analysis of non-Markovian BSDEs and applications to biology and finance

20. L. Neufcourt and F. Viens (2016): A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences

21. L. Neufcourt and F. Viens (2016): A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences

22. T. D. Nguyen (2016): Gaussian density estimates for the solution of singular stochastic Riccati equations, Appl Math 61, pp. 515-526

23. M. Rossi (2016): The Defect of Random Hyperspherical Harmonics

24. T. Sottinen and L. Viitasaari (2016): Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise

#### Year 2015

1. E. Azmoodeh and G. Peccati (2015): Optimal Berry-Esseen bounds on the Poisson space

2. S. Bachmann and G. Peccati (2015): Concentration Bounds for Geometric Poisson Functionals: Logarithmic Sobolev Inequalities Revisited

3. S. Bai and M. S. Taqqu (2015): The universality of homogeneous polynomial forms and critical limits, J. Theoret. Probab., to appear

4. S. Bai, M. S. Ginovyan and M. S. Taqqu (2015): Functional Limit Theorems for Toeplitz Quadratic Functionals of Continuous time Gaussian Stationary Processes

5. V. Bally and L. Caramellino (2015): An invariance principle for stochastic series I. Gaussian limits

6. E. del Barrio (2015): Berry-Esseen bounds for weighted averages of Poisson avoidance functionals

7. S. Bourguin (2015): Vector-valued semicircular limits on the free Poisson chaos

8. S. Campese (2015): Fourth Moment Theorems for complex Gaussian approximation

9. S. Campese, I. Nourdin, G. Peccati and G. Poly (2015): Multivariate Gaussian approximations on Markov chaoses

10. F. Caravenna, R. Sun and N. Zygouras (2015): Universality in marginally relevant disordered systems

11. L. H. Y. Chen (2015): Stein meets Malliavin in normal approximation, Acta Math. Vietnam. 40, 205-230.

12. L. H. Y. Chen and G. Poly (2015): Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem, Festschrift Masatoshi Fukushima (Z-Q Chen, N. Jacob, M. Takeda and T. Uemura, eds.), Interdisciplinary Mathematical Sciences Vol. 17, World Scientific, 107-130.

13. P.-C. Chu (2015): Stein's Method, Malliavin Calculus, Lévy White Noise Analysis, and their Applications in Financial Mathematics, PhD Thesis, School of Mathematical Sciences, University of Nottingham.

14. F. Dalmao (2015): CLT for the zeros of Kostlan Shub Smale random polynomials

15. L. Decreusefond (2015): The Stein-Dirichlet-Malliavin method, ESAIM: Proceedings, EDP Sciences, 2015, pp.11

16. B. El Onsy, K. Es-Sebaiy and F. G. Viens (2015): Parameter Estimation for a partially observed Ornstein-Uhlenbeck process with long-memory noise

17. K. Es-Sebaiy and F.G. Viens (2015): Parameter estimation for SDEs related to stationary Gaussian processes

18. T. Fissler and C. Thaele (2015): A four moments theorem for Gamma limits on a Poisson chaos

19. D. Harnett and D. Nualart (2015): Central limit theorem for functionals of a generalized self-similar process

20. A. Jaramillo and D. Nualart (2015): Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion

21. Y. Kim and H. Park (2015): Convergence rate of maximum likelihood estimator of parameter in stochastic partial differential equation, J. Korean Statist. Soc., in press

22. Y. Kim and H. Park (2015): Convergence rate of CLT for the estimation of Hurst parameter of fractional Brownian motion, Statist. Probab. Lett., in press

23. Y. Kim and H. Park (2015): Kolmogorov distance for the central limit theorems of the Wiener chaos expansion and applications, J. Korean Statist. Soc., in press

24. Y. Kim and H. Park (2015): Kolmogorov distance for multivariate normal approximation, Korean J. Math. 23, no. 1, pp. 1-10

25. K. Krokowski, A. Reichenbachs and C. Thaele (2015): Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs, point processes and percolation

26. S. Kusuoka and C.A. Tudor (2015): Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions

27. R. Lachèze-Rey and M. Reitzner (2015): U-statistics in stochastic geometry, book chapter

28. J. Liu, D. Tang and Y. Cang (2015): Variations and estimators for self-similarity parameter of sub-fractional Brownian motion via Malliavin calculus, Communications in Statistics - Theory and Methods, in press

29. R. Malukas (2015): Limit theorems for H-variation of Gaussian processes, PhD thesis

30. J.-C. Mourrat and J. Nolen (2015): Scaling limit of the corrector in stochastic homogenization

31. G. Naitzat and R. J. Adler (2015): A central limit theorem for the Euler integral of a Gaussian random field

32. L.I. Nicolaescu (2015): Critical points of multidimensional random Fourier series: central limits

33. L.I. Nicolaescu (2015): Wiener chaos and limit theorems

34. I. Nourdin, D. Nualart and R. Zintout (2015): Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation

35. I. Nourdin, G. Peccati, G. Poly and R. Simone (2015): Multidimensional limit theorems for homogeneous sums: a general transfer principle

36. D. Nualart (2015): An Introduction to the Malliavin Calculus and Its Applications, Stochastic Equations for Complex Systems Mathematical Engineering 2015, pp 1-36

37. N. Privault and G.L. Torrisi (2015): The Stein and Chen-Stein methods for functionals of non-symmetric Bernoulli processes

38. M. Rossi (2015): On the High Energy Behavior of Nonlinear Functionals of Random Eigenfunctions on Sd, Chapter of the forthcoming book Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry edited by G. Peccati and M. Reitzner

39. M. Schulte and C. Thaele (2015): Poisson point process convergence and extreme values in stochastic geometry, Chapter of the forthcoming book Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry edited by G. Peccati and M. Reitzner

40. R. Simone (2015): Universality and Fourth Moment Theorem for homogeneous sums. Orthogonal polynomials and apolarity, PhD thesis, Universita Degli Studi Della Basilicata, Potenza, Italy

41. G. Torrisi (2015): Gaussian approximation of nonlinear Hawkes processes, Ann. Applied Probab., to appear

42. G. Torrisi (2015): Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes, Ann. IHP Proba Stat, to appear

#### Year 2014

1. O. Arizmendi and A. Jaramillo (2014): Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates

2. J.-M. Azaïs, F. Dalmao and J.R. Leon (2014): CLT for the zeros of Classical Random Trigonometric Polynomials

3. E. Azmoodeh, G. Peccati and G. Poly (2014): The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

4. E. Azmoodeh, G. Peccati and G. Poly (2014): Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach

5. E. Azmoodeh, T. Sottinen and L. Viitasaari (2014): Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model

6. V. Benes and M. Zikmundova (2014): Functionals of spatial point processes having a density with respect to the Poisson process, Kybernetika 50, no. 6, pp. 896-913

7. S. Bourguin, C. Durastanti, D. Marinucci and G. Peccati (2014): Gaussian approximations of nonlinear statistics on the sphere

8. Y. Chen (2014): Product formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito Integrals

9. Y. Chen and Y. Liu (2014): On the fourth moment theorem for the complex multiple Wiener-Itô integrals

10.  P. Eichelsbacher and C. Thäle (2014): Malliavin-Stein method for Variance-Gamma approximation on Wiener space

11. A. Estrade and J.R. Leon (2014): A central limit theorem for the Euler characteristic of a Gaussian excursion set

12. L. Goldstein, I. Nourdin and G. Peccati (2014): Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula

13. Y. Hu, Y. Liu and D. Nualart (2014): Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions

14. Y. Hu, D. Nualart, S. Tindel and F. Xu (2014): Density convergence in the Breuer-Major theorem for Gaussian stationary sequences

15. K. Kamatani (2014): Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution

16. Y. T. Kim (2014): Weak convergence for multiple stochastic integrals in Skorohod space, Korean J. Math. 22, no. 1, pp. 71-84

17. K. Krokowski, A. Reichenbachs and C. Thaele (2014): Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

18. N. Kuang and B. Li (2014): Parameter estimations for the sub-fractional Brownian motion with drift at discrete observation, Brazilian Journal of Probability and Statistics, to appear

19. G. Last (2014): Stochastic analysis for Poisson processes

20. G. Last, G. Peccati and M. Schulte (2014): Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization

21. M. Ledoux, I. Nourdin and G. Peccati (2014): Stein's method, logarithmic Sobolev and transport inequalities, GAFA, to appear

22. J. Liu and L. Yan (2014): Solving a nonlinear fractional stochastic partial differential equation with fractional noise, J. Theoret. Probab., to appear

23. D. Marinucci and M. Rossi (2014): Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on Sd

24. T. Mastrolia, D. Possamaï and A. Réveillac (2016): Density analysis of BSDEs, Ann. Probab 44, no. 4, pp. 2817-2857

25. I. Nourdin, D. Nualart and G. Peccati (2014): Strong asymptotic independence on Wiener chaos

26. I. Nourdin, G. Peccati, G. Poly and R. Simone (2014): Classical and free fourth moment theorems: universality and thresholds

27. D. Nualart (2014): Normal Approximation on a Finite Wiener Chaos, Stochastic Analysis and Applications 2014, Springer Proceedings in Mathematics and Statistics Volume 100, 2014, pp 377-395

28. C. Olivera and C.A. Tudor (2014): The density of the solution to the stochastic transport equation with fractional noise

29. M. S. Pakkanen and A. Réveillac (2014): Functional limit theorems for generalized variations of the fractional Brownian sheet

30. G. Peccati (2014): Quantitative CLTs on a Gaussian space: a survey of recent developments. ESAIM: PROCEEDINGS 44, pp. 61-78

31. M.D. Ruiz-Medina and R.M. Crujeiras (2014): A Central Limit Result in the Wavelet Domain for Minimum Contrast Estimation of Fractal Random Fields. Theory Probab. Appl. 58, no. 3, 458-486.

32. M. Schulte and C. Thaele (2014): Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem

33. R. Simone (2014): Universality of free homogeneous sums in every dimension

34. C.A. Tudor (2014): Chaos expansion and asymptotic behavior of the Pareto distribution, Statist. Probab. Lett., to appear

35. D. Yogeshwaran, E. Subag and R.J. Adler (2014): Random geometric complexes in the thermodynamic regime

#### Year 2013

1. O. Arizmendi (2013): Convergence of the fourth moment and infinite divisibility

2. J.-M. Azaïs and J.R. León (2013): CLT for crossing of random trigonometric polynomials, Electron. J. Probab. 18, no. 68, 1-17.

3. E. Azmoodeh, S. Campese and G. Poly (2013): Fourth Moment Theorems for Markov Diffusion Generators

4. E. Azmoodeh, D. Malicet and G. Poly (2013): Generalization of the Nualart-Peccati criterion

5. E. Azmoodeh and J.I. Morlanes (2013): Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind

6. E. Azmoodeh and L. Viitasaari (2013): Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind

7. J.-M. Bardet and C.A. Tudor (2013): Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

8. V.I. Bogachev, E. D. Kosov, I. Nourdin and G. Poly (2013): Two properties of vectors of quadratic forms in Gaussian random variables

9. S. Bourguin (2013): Poisson convergence on the free Poisson algebra

10. S. Bourguin and G. Peccati (2013): Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle

11. V. Cammarota and D. Marinucci (2013): On the Limiting Behaviour of Needlets Polyspectra

12. A. De, I. Diakonikolas and R. Servedio (2013): Deterministic Approximate Counting for Juntas of Degree-2 Polynomial Threshold Functions

13. A. De and R. Servedio (2013): Efficient deterministic approximate counting for low-degree polynomial threshold functions

14. A. Deya, D. Nualart and S. Tindel (2013): On L2 modulus of continuity of Brownian local times and Riesz potentials

15. P. Eichelsbacher and C. Thaele (2013): New Berry-Esseen bounds for non-linear functionals of Poisson random measures

16. D. Harnett and D. Nualart (2013): On Simpson's rule and fractional Brownian motion with H = 1/10

17. Y. Hu, F. Lu and D. Nualart (2013): Convergence of densities of some functionals of Gaussian processes

18. D. Hug, G. Last and M. Schulte (2013): Second order properties and central limit theorems for geometric functionals of Boolean models

19. A. V. Ivanov, N. Leonenko, M. D. Ruiz-Medina, I. N. Savich (2013): Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra, Ann. Probab. 41, no. 2, 1088-1114

20. Y. Kim (2013): A sufficient condition on optimal Berry-Esseen bounds of functionals of Gaussian fields, Communications for Statistical Applications and Methods 20, no.1, 15-22

21. S. Kusuoka and C.A. Tudor (2013): Extension of the Fourth Moment Theorem to invariant measures of diffusions

22. N. Marie (2013): Ergodicity of a Generalized Jacobi's Equation and Applications

23. B. Maslowski and C.A. Tudor (2013): Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process, to appear in Bulletin des Sciences Mathématiques.

24. N. Naganuma (2013): Asymptotic error distributions of the Crank-Nicholson scheme for SDEs driven by fractional Brownian motion, poster in the 5th GCOE International Symposium on "Weaving Science Web beyond Particle-Matter Hierarchy", March 4-6, Sendai, Japan

25. I. Nourdin and D. Nualart (2013): Fisher Information and the Fourth Moment Theorem

26. I. Nourdin, D. Nualart and G. Peccati (2013): Quantitative stable limit theorems on the Wiener space, Ann. Probab., to appear

27. I. Nourdin, G. Peccati and Y. Swan (2013): Entropy and the fourth moment phenomenon

28. I. Nourdin and G. Peccati (2013): The optimal fourth moment theorem, Proc. of the A.M.S., to appear

29. I. Nourdin, G. Peccati and F.G. Viens (2013): Comparison inequalities on Wiener space

30. I. Nourdin and G. Poly (2013): An invariance principle under the total variation distance

31. I. Nourdin and R. Zeineddine (2014): An Itô's type formula for the fractional Brownian motion in Brownian time, Electron. J. Probab. 19, no. 99, pp. 1-15.

32. I. Nourdin and R. Zintout (2013): Cross-variation of Young integral with respect to long-memory fractional Brownian motions, Probab. Math. Statist., to appear

33. D. Nualart (2013): Book Review of Normal approximations with Malliavin calculus. From Stein’s method to universality by Ivan Nourdin and Giovanni Peccati, Bulletin of the AMS

34. D. Nualart and J. Swanson (2013): Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II

35. E. Nualart and F.G. Viens (2013): Hitting probabilities for general Gaussian processes

36. M. S. Pakkanen (2013): Limit theorems for power variations of ambit fields driven by white noise

37. G. Peccati and C. Thaele (2013): Gamma limits and U-statistics on the Poisson space

38. N. Privault and G.L. Torrisi (2013): Probability approximation by Clark-Ocone covariance representation, Electron. J. Probab. 18, no. 91, pp. 1-25.

39. M. Reitzner, M. Schulte and C. Thaele (2013): Limit theory for the Gilbert graph.

40. R. Speicher (2013): Asymptotic Eigenvalue Distribution of Random Matrices and Free Stochastic Analysis, Random Matrices and Iterated Random Functions, Springer Proceedings in Mathematics and Statistics 53, pp 31-44

41. S. Torres, C.A. Tudor and F.G. Viens: Quadratic variations for the fractional-colored stochastic heat equation, Electron. J. Probab. 19 (2014), no. 76, 1–51

42. C.A. Tudor (2013): Analysis of variations for self-similar processes, Springer, Probability and Its Applications.

43. R. Zeineddine (2013): Fluctuations of the power variation of fractional Brownian motion in Brownian time

#### Year 2012

1. S. Aazizi and K. Es-Sebaiy (2012): Berry-Esseen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion.

2. F. Avram, N. Leonenko and L. Sakhno (2012): Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities.

3. S. Bai and M. S. Taqqu (2012): Multivariate limit theorems in the context of long-range dependence.

4. J.-M. Bardet and D. Surgailis (2012): Moment bounds and central limit theorems for Gaussian subordinated arrays, J. Multi. Anal., to appear

5. H. Biermé, A. Bonami, I. Nourdin and G. Peccati (2012): Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants, ALEA 9 (2), 473-500

6. S. Bourguin and J.-C. Breton (2012): Asymptotic Cramér type decomposition for Wiener and Wigner integrals, Infinite Dimensional Analysis, Quantum Probability and Related Topics, to appear

7. S. Bourguin and G. Peccati: Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering, Electron. J. Probab. 19 (2014), no. 66, 1–42

8. J.-C. Breton and J.-F. Coeurjolly (2012): Refined non-asymptotic confidence intervals for the Hurst parameter of a fractional Brownian motion, Stat. Inference Stoch. Process, to appear

9. K. Burdzy, D. Nualart and J. Swanson (2012): Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion

10. P. Cénac and K. Es-Sebaiy (2012): Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes

11. J.M. Corcuera, E. Hedevang, M.S. Pakkanen and M. Podolskij (2012): Asymptotic theory for Brownian semi-stationary processes with application to turbulence

12. L. Decreusefond, E. Ferraz, P. Martins and T. Vu (2012): Robust methods for LTE and WiMAX dimensioning

13. A. Deya, S. Noreddine and I. Nourdin (2012): Fourth Moment Theorem and q-Brownian Chaos, Comm. Math. Phys., to appear.

14. A. Deya and I. Nourdin (2012): Convergence of Wigner integrals to the tetilla law, ALEA 9, 101-127.

15. C. Durastanti, X. Lan and D. Marinucci (2012): Needlet-Whittle Estimates on the Unit Sphere. .

16. C. Durastanti, D. Marinucci and G. Peccati (2012): Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields. .

17. R. Eden and J. Víquez (2012): Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions

18. D. Harnett and D. Nualart (2012): CLT for an iterated integral with respect to fBm with H>1/2

19. J. Istas (2012): Estimating self-similarity through complex variations, Electron. J. Statist. 6, 1392-1408

20. T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012): Wigner chaos and the fourth moment, Ann. Probab. 40, no. 4, 1577-1635.

21. S. Kusuoka (2012): Survey on the fourth moment theorem, Stein's method and related topics, Tohoku University

22. S. Kusuoka and C.A. Tudor (2012): Stein's method for invariant measures of diffusions via Malliavin calculus, Stoch. Proc. Appl. 122 (4), 1627–1651.

23. R. Lachieze-Rey and G. Peccati (2012): Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics

24. G. Last, M. D. Penrose, M. Schulte and C. Thaele (2012): Moments and central limit theorems for some multivariate Poisson functionals

25. D. Marinucci and I. Wigman (2012): On Nonlinear Functionals of Random Spherical Eigenfunctions

26. M. Moers (2012): Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model, International Journal of Stochastic Analysis, article ID 268568.

27. I. Nourdin (2012): Selected aspects of fractional Brownian motion, Springer Verlag (Bocconi and Springer Series), to appear.

28. I. Nourdin (2012): Lectures on Gaussian approximations with Malliavin calculus, Prix de la Fondation des Sciences Mathématiques de Paris

29. I. Nourdin, D. Nualart and G. Poly (2012): Absolute continuity and convergence of densities for random vectors on Wiener chaos

30. I. Nourdin and G. Peccati (2012): Normal approximations with Malliavin calculus: from Stein's method to universality. Cambridge University Press (Cambridge Tracts in Mathematics)

31. I. Nourdin and G. Poly (2012): Convergence in law in the second Wiener/Wigner chaos, Elect. Comm. in Probab. 17, no. 36.

32. I. Nourdin and G. Poly (2012): Convergence in total variation on Wiener chaos, Stoch. Proc. Appl., to appear

33. M. Schulte (2012): A Central Limit Theorem for the Poisson-Voronoi Approximation, Adv. Appl. Math. 49, no. 3-5, 285-306

34. M. Schulte (2012): Normal approximation of Poisson functionals in Kolmogorov distance

35. M. Schulte and C. Thaele (2012): The scaling limit of Poisson-driven order statistics with applications in geometric probability, Stoch. Proc. Appl. 122, no. 12, 4096-4120

36. M. Schulte and C. Thaele (2012): Distances between Poisson k-flats

#### Year 2011

1. O. Aboura and S. Bourguin: Density estimates for solutions to one dimensional backward SDE's. Potential Analysis 38, no. 2 (2013), pp 573-587

2. O. E. Barndorff-Nielsen, J. M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semi-stationary processes, Bernoulli 17, no. 4, 1159-1194.

3. H. Biermé, A. Bonami and J.R. León (2011): Central limit theorems and quadratic variations in terms of spectral density, Electron. J. Probab. 16, no. 13, 362-395

4. S. Bourguin and C.A. Tudor: Malliavin Calculus and Self Normalized Sums, Séminaire de Probabilités XLV, Lecture Notes in Mathematics 2013, pp 323-351

5. S. Bourguin and C.A. Tudor (2011): Berry-Esseen bounds for long memory moving averages via Stein's method and Malliavin calculus. Stoch. Anal. Appl. 29, no. 5, 881-905

6. S. Bourguin and C.A. Tudor (2011): Cramér's theorem for Gamma random variables, Electron. Comm. Probab. 16, no. 1, 365-378.

7. L. H. Y. Chen, L. Goldstein and Q.-M. Shao (2011): Normal Approximation by Stein’s Method, Probability and Its Applications, Springer-Verlag (see more precisely the chapter 14, entitled ``Group Characters and Malliavin Calculus'')

8. J.M. Corcuera (2011): New Central Limit Theorems for Functionals of Gaussian Processes and their Applications. Methodol. Comput. Appl. Probab. (online first)

9. L. Decreusefond, E. Ferraz and H. Randriam: Simplicial Homology of Random Configurations, Journal of Advances in Applied Probability, Mars 2013

10. A. Deya and I. Nourdin: Invariance principles for homogeneous sums of free random variables, Bernoulli 20, no. 2 (2014), 586-603

11. C. Durastanti, X. Lan and D. Marinucci: Gaussian Semiparametric Estimates on the Unit Sphere, Bernoulli 20, no. 1 (2014), 28-77

12. K. Es-Sebaiy and C.A. Tudor (2011): Noncentral limit theorem for the cubic variation of a class of self-similar stochastic processes, Theory Probab. Appl. 55, no. 3, 411-431.

13. E. Ferraz and A. Vergne (2011): Statistics of geometric random simplicial complexes

14. Y. Hu, D. Nualart, X. Weilin and Z. Weiguo (2011): Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation, Acta Math. Scientia 31B, no. 5, 1851-1859

15. R. Lachieze-Rey and G. Peccati: Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs, Electron. J. Probab. 18 (2013), no. 32, 1–32.

16. D. Marinucci and G. Peccati (2011): Random fields on the Sphere. Representation, Limit Theorems and Cosmological Applications. Series: London Mathematical Society Lecture Note Series 389. Cambridge University Press.

17. S. Noreddine and I. Nourdin (2011): On the Gaussian approximation of vector-valued multiple integrals, J. Multiv. Anal. 102, no. 6, 1008-1017.

18. I. Nourdin (2011): Yet another proof of the Nualart-Peccati criterion, Electron. Comm. Probab. 16, 467-481

19. I. Nourdin and G. Peccati: Poisson approximations on the free Wigner chaos, Ann. Probab. 41, no. 4 (2013), 2709-2723

20. I. Nourdin, G. Peccati and M. Podolskij (2011): Quantitative Breuer-Major theorems. Stoch. Proc. Appl. 121, no. 4, 793-812.

21. I. Nourdin, G. Peccati and R. Speicher: Multidimensional semicircular limits on the free Wigner chaos, Seminar on Stochastic Analysis, Random Fields and Applications VII, Progress in Probability 67, 2013, pp 211-221

22. I. Nourdin and J. Rosiński: Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws, Ann. Probab. 42, no. 2 (2014), 497-526

23. I. Nourdin and M.S. Taqqu (2011): Central and non-central limit theorems in a free probability setting, J. Theoret. Probab. 27, no. 1, 220-248

24. D. Nualart and L. Quer-Sardanyons (2011): Optimal Gaussian density estimates for a class of stochastic equations with additive noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, 25-34.

25. H.S. Park, J.W. Jeon and Y.T. Kim (2011): The central limit theorem for cross-variation related to the standard Brownian sheet and Berry–Esseen bounds, J. Korean Statist. Soc. 40, no. 2, 239-244

26. G. Peccati (2011): The Chen-Stein method for Poisson functionals

27. G. Peccati and C. Zheng: Universal Gaussian fluctuations on the discrete Poisson chaos, Bernoulli 20, no. 2 (2014), 697-715

28. M. Reitzner and M. Schulte: Central Limit Theorems for U-Statistics of Poisson Point Processes, Ann. Probab. 41, no. 6 (2013), 3879-3909

29. C. Tudor (2011): Berry–Esséen bounds and almost sure CLT for the quadratic variation of the sub-fractional Brownian motion, J. Math. Anal. Appl. 375, no. 2, 667-676.

30. C.A. Tudor (2011): Asymptotic Cramér's theorem and analysis on Wiener space, Séminaire de Probabilités XLIII, Lecture Notes in Mathematics, 309-325

#### Year 2010

1. H. Airault, P. Malliavin and F.G. Viens (2010): Stokes formula on the Wiener space and n-dimensional Nourdin–Peccati analysis, J. Funct. Anal. 258, 1763-1783

2. B. Bercu, I. Nourdin and M.S. Taqqu (2010): Almost sure central limit theorems on the Wiener space , Stoch. Proc. Appl. 120, no. 9, 1607-1628

3. V. Bogachev (2010): Differentiable Measures and the Malliavin Calculus, American Mathematical Society (see more precisely pages 321-323)

4. S. Darses, I. Nourdin and D. Nualart (2010): Limit theorems for nonlinear functionals of Volterra processes via white noise analysis, Bernoulli 16, no. 4, 1262-1293

5. R. Eden and F.G. Viens: General upper and lower tail estimates using Malliavin calculus and Stein's equations, Seminar on Stochastic Analysis, Random Fields and Applications VII Progress in Probability Volume 67, 2013, pp 55-84

6. Y. Hu and D. Nualart (2010): Parameter estimation for fractional Ornstein-Uhlenbeck processes, Stat. Probab. Lett. 80, no. 11-12, 1030-1038

7. M. Ledoux: Chaos of a Markov operator and the fourth moment condition, Ann. Probab. 40, no. 6, 2012, 2439-2459

8. D. Marinucci and I. Wigman: On the Excursion Sets of Spherical Gaussian Eigenfunctions, Journal of Mathematical Physics, 52, 9, 093301, 21 pp. (2011)

9. D. Marinucci and G. Peccati (2010): Ergodicity and Gaussianity for Spherical Random Fields, J. Math. Phys. 51, 043301

10. D. Marinucci and G. Peccati (2010): Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli 16, no. 3, 798-824.

11. A. Neuenkirch, S. Tindel and J. Unterberger (2010): Discretizing the fractional Levy area, Stoch. Proc. Appl. 120, no. 2, 223-254

12. I. Nourdin and D. Nualart (2010): Central limit theorems for multiple Skorohod integrals, J. Theoret. Probab. 23, no. 1, 39-64

13. I. Nourdin, D. Nualart and C.A. Tudor (2010): Central and non-central limit theorems for weighted power variations of fractional Brownian motion, Ann. I.H.P. 46, no. 4, 1055-1079

14. I. Nourdin and G. Peccati (2010): Stein's method meets Malliavin calculus: a short survey with new estimates, In the volume: Recent Advances in Stochastic Dynamics and Stochastic Analysis, World Scientific

15. I. Nourdin and G. Peccati (2010): Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs, ALEA 7, 341-375

16. I. Nourdin and G. Peccati (2010): Cumulants on the Wiener space, J. Funct. Anal. 258, 3775-3791

17. I. Nourdin and G. Peccati (2010): Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields, Ann. Probab. 37, no. 6, 2231-2261

18. I. Nourdin, G. Peccati and G. Reinert (2010): Stein's method and stochastic analysis of Rademacher sequences, Elect. J. Probab. 15, no. 55, 1703-1742

19. I. Nourdin, G. Peccati and G. Reinert (2010): Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos, Ann. Probab. 38, no. 5, 1947-1985

20. I. Nourdin, G. Peccati and A. Réveillac (2010): Multivariate normal approximation using Stein's method and Malliavin calculus, Ann. I.H.P. 46, no. 1, 45-58

21. I. Nourdin, A. Réveillac and J. Swanson (2010): The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. Elect. J. Probab. 15, 2117-2162.

22. G. Peccati, J.-L. Solé, M.S. Taqqu and F. Utzet (2010): Stein's method and normal approximation of Poisson functionals, Ann. Probab. 38, no. 2, 443-478

23. G. Peccati and M.S. Taqqu (2010): Wiener Chaos: Moments, Cumulants and Diagrams, Springer Verlag (Bocconi and Springer Series) (see more precisely the chapter 11, entitled ``Limit theorems on the Gaussian Wiener chaos'')

24. G. Peccati and C. Zheng (2010): Multi-dimensional Gaussian fluctuations on the Poisson space, Elect. J. Probab. 15, no. 48, 1487-1527

25. A. Réveillac, M. Stauch and C.A. Tudor: Hermite variations of the fractional Brownian sheet. Stoch. Dyn. 12(3), 1150021 (2012), 21 pp

26. M. Schulte and C. Thaele (2010): Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes

#### Year 2009

1. P. Baldi, G. Kerkyacharian, D. Marinucci and D. Picard (2009): Asymptotics for spherical needlets, Ann. Statist. 37, no. 3, 1150-1171.

2. O. E. Barndorff-Nielsen, J. M. Corcuera and M. Podolskij (2009): Power variation for Gaussian processes with stationary increments, Stoch. Proc. Appl. 119, 1845-1865

3. O. E. Barndorff-Nielsen, J. M. Corcuera, M. Podolskij and J. H. C. Woerner (2009): Bipower variation for Gaussian processes with stationary increments, J. Appl. Probab. 46, 132-150

4. J.-C. Breton, I. Nourdin and G. Peccati (2009): Exact confidence intervals for the Hurst parameter of a fractional Brownian motion, Electron. J. Statist. 3, 416-425

5. B. Buchmann and N. H. Chan (2009): Integrated functionals of normal and fractional processes, Ann. Appl. Probab. 19, no. 1, 49-70.

6. X. Lan and D. Marinucci (2009): On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields, Stoch. Proc. Appl. 119 3749-3766

7. I. Nourdin (2009): A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4, J. Funct. Anal. 256, 2303-2320

8. I. Nourdin and G. Peccati (2009): Non-central convergence of multiple integrals, Ann. Probab. 37, no. 4, 1412–1426

9. I. Nourdin and G. Peccati (2009): Stein's method on Wiener chaos, Probab. Theory Rel. Fields 145, no. 1, 75-118

10. I. Nourdin, G. Peccati and G. Reinert (2009): Second order Poincaré inequalities and CLTs on Wiener space, J. Funct. Anal. 257, 593-609

11. I. Nourdin and A. Réveillac (2009): Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4, Ann. Probab. 37, no. 6, 2200-2230

12. I. Nourdin and F.G. Viens (2009): Density formula and concentration inequalities with Malliavin calculus, Electron. J. Probab. 14, 2287-2309

13. D. Nualart (2009): Malliavin Calculus and Its Applications, American Mathematical Society and CBMS Regional Conference Series in Mathematics (see more precisely the chapter 9, entitled ``Central limit theorem and Malliavin calculus'')

14. D. Nualart and L. Quer-Sardanyons (2009): Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations. Stoch. Proc. Appl. 119, 3914-3938.

15. G. Peccati (2009): Stein's method, Malliavin calculus and infinite-dimensional Gaussian analysis, Progress in Stein’s Method, Singapore

16. Surveys in stochastic processes, 107–126, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2011

17. A. Réveillac (2009): Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheets, Stoch. Anal. Appl. 27, no. 1, 51-73

18. S. Si (2009): Two-step variations for processes driven by fractional Brownian motion with application in testing for jumps from the high frequency data, PhD thesis, University of Tennessee

19. C.A. Tudor (2009): Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion, Elect. Comm. in Probab. 14, 278–289

20. F.G. Viens (2009): Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent, Stoch. Proc. Appl. 119, 3671-3698

#### Year 2008

1. J.-C. Breton and I. Nourdin (2008): Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion, Electron. Comm. in Probab. 13, 482-493

2. X. Lan and D. Marinucci (2008): The needlets bispectrum, Electron. J. Statist. 2, 332-367

3. D. Marinucci and G. Peccati (2008): High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group, Stoch. Proc. Appl. 118, no. 4, 585-613

4. I. Nourdin and G. Peccati (2008): Weighted power variations of iterated Brownian motion, Elect. J. Probab. 13, no. 43, 1229-1256

5. D. Nualart and S. Ortiz-Latorre (2008): Central limit theorems for multiple stochastic integrals and Malliavin calculus, Stoch. Proc. Appl. 118, no. 4, 614-628

#### Year 2007

1. A. Neuenkirch and I. Nourdin (2007): Exact rate of convergence of some approximation schemes associated to SDEs driven by a fBm. J. Theoret. Probab. 20, 871-899

2. G. Peccati (2007): Gaussian approximations of multiple integrals, Elect. Comm. in Probab. 12, 350-364

#### Year 2006

1. J.M. Corcuera, D. Nualart and J.H.C. Woerner (2006): Power variation of some integral fractional processes, Bernoulli 12, no. 4, 713-735

#### Year 2005

1. Y. Hu and D. Nualart (2005): Renormalized self-intersection local time for fractional Brownian motion, Ann. Probab. 33, no. 3, 948-983

#### Year 2004

1. G. Peccati and C.A. Tudor (2004): Gaussian limits for vector-valued multiple stochastic integrals, Séminaire de Probabilités XXXVIII, 247-262

2. D. Nualart and G. Peccati (2005): Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33, no. 1, 177-193