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 ressources 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 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, preprint

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

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

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

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

  6. C. Doebler and G. Peccati (2017): The fourth moment theorem on the Poisson space, preprint

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

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

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

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

  11. 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

  12. 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

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

  14. C. Krein (2017): Weak convergence on Wiener space: targeting the first two chaoses, preprint

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

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

  17. I. Nourdin and G. Zheng (2017): Exchangeable pairs on Wiener chaos, preprint

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

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

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

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, preprint

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

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

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

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

  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, preprint

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

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

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

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

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

  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, preprint

  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, preprint

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

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

  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, preprint

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

  25. G. Torrisi (2016): Probability approximation of point processes with Papangelou conditional intensity, preprint

  26. C. Tudor (2016): Multidimensional Selberg theorem and fluctuations of the zeta zeros via Malliavin calculus, preprint

  27. R. Zeineddine (2016): Asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time, preprint

  28. G. Zheng (2016): Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals, preprint

Year 2015

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

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

  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, preprint

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

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

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

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

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

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

  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, preprint

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

  16. C. Durastanti (2015): Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields, preprint

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

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

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

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

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

  22. 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

  23. 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

  24. 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

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

  26. K. Krokowski (2015): Poisson approximation of Rademacher functionals by the Chen-Stein method and Malliavin calculus, preprint

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

  28. 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, preprint

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

  30. 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

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

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

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

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

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

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

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

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

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

  40. 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

  41. 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

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

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

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

  45. L. Viitasaari (2015): Sufficient and Necessary Conditions for Limit Theorems for Quadratic Variations of Gaussian Sequences, preprint

Year 2014

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

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

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

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

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

  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, preprint

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

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

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

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

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

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

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

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

  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, preprint

  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, preprint

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

  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, preprint

  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, preprint

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

  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, preprint

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

  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, preprint

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

  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, preprint

  36. R. Zeineddine (2014): Change-of-variable formula for the bi-dimensional fractional Brownian motion in Brownian time, preprint

Year 2013

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

  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, preprint

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

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

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

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

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

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

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

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

  12. S. Campese (2013): Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian Fields, preprint

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

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

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

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

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

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

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

  20. 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 

  21. 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

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

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

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

  25. 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

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

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

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

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

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

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

  32. 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.  

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

  34. 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

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

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

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

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

  39. V. H. Pham (2013): On the rate of convergence for central limit theorems of sojourn times of Gaussian fields, preprint

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

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

  42. 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

  43. 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

  44. C. A. Tudor (2013): The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals, preprint

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

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

Year 2012

  1. S. Aazizi (2012): A Simple Proof of Berry-Esséen Bounds for the Quadratic Variation of the Subfractional Brownian Motion. Preprint

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

  3. 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. Preprint

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

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

  6. 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

  7. 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

  8. 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

  9. 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

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

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

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

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

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

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

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

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

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

  19. K. Es-Sebaiy (2012): Berry-Esseen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes , Preprint

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

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

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

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

  24. 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.

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

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

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

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

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

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

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

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

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

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

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

  36. M. Schulte (2012): Normal approximation of Poisson functionals in Kolmogorov distance, preprint

  37. 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

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

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, Preprint

  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. M.T. Nguyen (2011): Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes, preprint

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

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

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

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

  22. 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

  23. 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

  24. 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

  25. 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.

  26. 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

  27. G. Peccati (2011): The Chen-Stein method for Poisson functionals, Preprint

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

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

  30. 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.

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

  32. J. Víquez (2011): On the second order Poincaré inequality and CLT on Wiener-Poisson space, Preprint

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, Preprint

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. G. Reinert: Gaussian approximation of functionals: Malliavin calculus and Stein’s method, 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