My publications
My books (Link towards the dedicated page)
#2: I. Nourdin and G. Peccati (2012): Normal approximations with Malliavin calculus: from Stein's method to universality. Cambridge Tracts in Mathematics 192. Cambridge University Press, Cambridge, 2012. xiv+239 pp.
(This book won the 2015 FNR Award for outstanding scientific publication.)
#1: I. Nourdin (2012): Selected aspects of fractional Brownian motion. Bocconi & Springer Series 4. Springer, Milan; Bocconi University Press, Milan, 2012. x+122 pp
My book chapters
#1: I. Nourdin (2012): Lectures on Gaussian approximations with Malliavin calculus. Sém. Probab. XLV, pp. 3-89. To pdf file
My preprints and published papers
#111: N. Leonenko, L. Maini, I. Nourdin and F. Pistolato (2024): Limit theorems for p-domain functionals of stationary Gaussian fields. Preprint. To pdf file
#110: S. Favaro, B. Hanin, D. Marinucci, I. Nourdin and G. Peccati (2023): Quantitative CLTs in Deep Neural Networks. Preprint. To pdf file
#109: V. Garino and I. Nourdin (2023): Total variation bound for Hadwiger's functional using Stein's method. Preprint. To pdf file
#108: L. Maini and I. Nourdin (2024): Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields. Ann. Probab. 52, no. 2, pp. 737-763. To pdf file
#107: A. Jaramillo, I. Nourdin, D. Nualart and G. Peccati (2023): Limit theorems for additive functionals of the fractional Brownian motion. Ann. Probab. 51, no. 3, pp. 1066-1111. To pdf file
#106: I. Nourdin and F. Pu (2022): Gaussian fluctuation for Gaussian Wishart matrices of overall correlation. Statist. Probab. Letters 181, 109269. To pdf file
#105: S. Douissi, K. Es-Sebaiy, G. Kerchev and I. Nourdin (2022): Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency. Electron. J. Statist. 16, no. 1, pp. 636-670. To pdf file
#104: V. Garino, I. Nourdin, D. Nualart and M. Salamat (2021): Limit theorems for integral functionals of Hermite-driven processes. Bernoulli 27, no. 3, pp. 1764-1788. To pdf file
#103: G. Dierickx, I. Nourdin, G. Peccati and M. Rossi (2023): Small Scale CLTs for the Nodal Length of Monochromatic Waves. Comm. Math. Phys. 397, pp. 1-36. To pdf file
#102: G. Kerchev, I. Nourdin, E. Saksman and L. Viitasaari (2021): Local times and sample path properties of the Rosenblatt process. Stoch. Proc. Appl. 131, pp. 498-522. To pdf file
#101: V. Garino, I. Nourdin and P. Vallois (2022): Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion. Electron. J. Probab. 27, pp. 1-43. To pdf file
#100: I. Nourdin, G. Peccati and X. Yang (2022): Multivariate normal approximation on the Wiener space: new bounds in the convex distance. J. Theoret. Probab. 35, pp. 2020-2037. To pdf file
#99: P. Chen, I. Nourdin, L. Xu and X. Yang (2019): Multivariate stable approximation in Wasserstein distance by Stein's method. J. Theoret. Probab., to appear. To pdf file
#98: I. Nourdin, D. Nualart and G. Peccati (2021): The Breuer-Major Theorem in total variation: improved rates under minimal regularity. Stoch. Proc. Appl. 131, pp. 1-20. To pdf file
#97: I. Nourdin, G. Peccati and X. Yang (2020): Restricted hypercontractivity on the Poisson space. Proc. of the A.M.S. 148, pp. 3617-3632 To pdf file
#96: P. Chen, I. Nourdin, L. Xu, X. Yang and R. Zhang (2022): Non-integrable stable approximation by Stein's method. J. Theoret. Probab. 35, pp. 1137-1186. To pdf file
#95: A. Jaramillo, I. Nourdin and G. Peccati (2021): Approximation of Fractional Local Times: Zero Energy and Weak Derivatives. Ann. Appl. Probab. 31, no. 5, pp. 2143-2191. To pdf file
#94: I. Nourdin, G. Peccati and X. Yang (2019): Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality. Electron. Comm. Probab. 24, paper no. 34, 12 pages. To pdf file
#93: M. Lotz, M.B. McCoy, I. Nourdin, G. Peccati and J.A. Tropp (2018): Concentration of the Intrinsic Volumes of a Convex Body. Geometric Aspects of Functional Analysis – Israel Seminar (GAFA) 2017-2019, Lecture Notes in Mathematics 2266. To pdf file
#92: I. Nourdin, G. Peccati and S. Seuret (2020): Sojourn time dimensions of fractional Brownian motion. Bernoulli 26, no. 3, pp. 1619-1634. To pdf file
#91: P. Chen, I. Nourdin and L. Xu (2021): Stein's method for asymmetric alpha-stable distributions, with application to the stable CLT. J. Theoret. Probab. 34, pp. 1382-1407. To pdf file
#90: I. Nourdin and D. Nualart (2020): The functional Breuer-Major theorem. Probab. Th. Related Fields 176, pp. 203-218. To pdf file
#89: S. Campese, I. Nourdin and D. Nualart (2020): Continuous Breuer-Major theorem: tightness and non-stationarity. Ann. Probab. 48, no. 1, pp. 147-177. To pdf file
#88: E. Azmoodeh and I. Nourdin (2019): Almost sure limit theorems on Wiener chaos: the non-central case. Electron. Comm. Probab. 24, paper no. 9, 1-12. To pdf file
#87: I. Nourdin and G. Zheng (2022): Asymptotic behavior of large Gaussian correlated Wishart matrices. J. Theoret. Probab. 35, pp. 2239-2268. To pdf file
#86: I. Nourdin and D. Tran (2019): Statistical inference for Vasicek-type model driven by Hermite processes. Stoch. Proc. Appl. 129, no. 10, pp. 3774-3791. To pdf file
#85: I. Nourdin, G. Peccati and M. Rossi (2019): Nodal Statistics of Planar Random Waves. Comm. Math. Phys. 369, no. 1, pp. 99-151. To pdf file
#84: I. Nourdin and G. Zheng (2019): Exchangeable pairs on Wiener chaos. High-Dimensional Probability VIII, pp. 277-303. To pdf file
#83: S. Bourguin and I. Nourdin (2020): Freeness characterizations on free chaos spaces. Pacific J. Math 305, no. 2, pp. 447-472. To pdf file
#82: F. Dalmao, I. Nourdin, G. Peccati and M. Rossi (2019): Phase singularities in complex arithmetic random waves. Electron. J. Probab. 24, no. 71, 45 pages. To pdf file
#81: A. Lechiheb, I. Nourdin, G. Zheng and E. Haouala (2018): Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization. Probab. Math. Stat. 38, no. 2, pp. 271-286. To pdf file
#80: G. Binotto, I. Nourdin and D. Nualart (2018): Weak symmetric integrals with respect to the fractional Brownian motion. Ann. Probab. 46, no. 4, pp. 2243-2267 To pdf file
#79: M. Ledoux, I. Nourdin and G. Peccati (2017): A Stein deficit for the logarithmic Sobolev inequality. Science China Mathematics 60, no. 7, pp. 1163-1180. To pdf file
#78: J.-M. Azaïs, F. Dalmao, J. León, I. Nourdin and G. Poly (2015): Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients. Preprint. To pdf file
#77: S. Campese, I. Nourdin, G. Peccati and G. Poly (2016): Multivariate Gaussian approximations on Markov chaoses. Electron. Commun. Probab. 21, paper no. 48. To pdf file
#76: I. Nourdin, G. Peccati, G. Poly and R. Simone (2016): Multidimensional limit theorems for homogeneous sums: a general transfer principle. ESAIM PS 20, pp. 293-308. To pdf file
#75: D. Malicet, I. Nourdin, G. Peccati and G. Poly (2016): Squared chaotic random variables: new moment inequalities with applications. J. Funct. Anal. 270, no. 2, pp. 649–670. To pdf file
#74: I. Nourdin, D. Nualart and R. Zintout (2016): Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation. Statist. Infer. Stoch. Proc. 19, no. 2, pp. 219-234. To pdf file
#73: L. Goldstein, I. Nourdin and G. Peccati (2017): Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula. Ann. Appl. Probab. 27, no. 1, pp. 1-47. To pdf file
#72: I. Nourdin, G. Peccati, G. Poly and R. Simone (2016): Classical and free fourth moment theorems: universality and thresholds. J. Theoret. Probab. 29, no. 2, pp. 653–680. To pdf file
#71: M. Ledoux, I. Nourdin and G. Peccati (2015): Stein's method, logarithmic Sobolev and transport inequalities. Geom. Funct. Anal. 25, no. 1, 256-306. To pdf file
#70: I. Nourdin, D. Nualart and G. Peccati (2016): Strong asymptotic independence on Wiener chaos. Proc. of the A.M.S. 144, no. 2, pp. 875-886. To pdf file
#69: I. Nourdin and D. Nualart (2016): Fisher information and the Fourth Moment Theorem. Ann. Inst. H. Poincaré Probab. Statist. 52, no. 2, pp. 849-867. To pdf file
#68: I. Nourdin, G. Peccati and Y. Swan (2014): Integration by parts and representation of information functionals. Proceedings of the 2014 IEEE International Symposium on Information Theory (ISIT), Conference Location: Honolulu, HI. Pages 2217-2221. To pdf file
#67: 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, 1-15. To pdf file
#66: I. Nourdin and R. Zintout (2016): Cross-variation of Young integral with respect to long-memory fractional Brownian motions. Probab. Math. Statist. 36, no. 35, pp. 35-46. To pdf file
#65: I. Nourdin and G. Poly (2015): An invariance principle under the total variation distance. Stoch. Proc. Appl. 125, no. 6, pp. 2190-2205. To pdf file
#64: I. Nourdin, G. Peccati and F.G. Viens (2014): Comparison inequalities on Wiener space. Stoch. Proc. Appl. 124, no. 4, 1566-1581. To pdf file
#63: V. Bogachev, E. Kosov, I. Nourdin and G. Poly (2014): Two properties of vectors of quadratic forms in Gaussian random variables. Teor. Veroyatnost. i Primenen 59, no. 2, 214-232. To pdf file
#62: I. Nourdin, D. Nualart and G. Peccati (2016): Quantitative stable limit theorems on the Wiener space. Ann. Probab. 44, no. 1, 1-41. To pdf file
#61: I. Nourdin and G. Poly (2016): Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables. High Dimensional Probability VII: The Cargèse Volume, Progress in Probability 71, Birkhäuser Basel, pp. 381-394. To pdf file
#60: I. Nourdin and G. Peccati (2015): The optimal fourth moment theorem. Proc. of the A.M.S. 143, no. 7, pp. 3123-3133. To pdf file
#59: I. Nourdin, G. Peccati and Y. Swan (2014): Entropy and the fourth moment phenomenon. J. Funct. Anal. 266, no. 5, 3170-3207. To pdf file
#58: I. Nourdin, D. Nualart and G. Poly (2013): Absolute continuity and convergence of densities for random vectors on Wiener chaos. Electron. J. Probab. 18, no. 22. To pdf file
#57: I. Nourdin and G. Poly (2013): Convergence in total variation on Wiener chaos. Stoch. Proc. Appl. 123, 651-674. To pdf file
#56: I. Nourdin and G. Poly (2012): Convergence in law in the second Wiener/Wigner chaos. Elect. Comm. in Probab. 17, paper no. 36. To pdf file
#55: A. Deya, S. Noreddine and I. Nourdin (2013): Fourth Moment Theorem and q-Brownian Chaos. Comm. Math. Phys. 321, no. 1, 113-134. To pdf file
#54: A. Deya and I. Nourdin (2014): Invariance principles for homogeneous sums of free random variables. Bernoulli 20, no. 2, 586-603. To pdf file
#53: I. Nourdin and J. Rosinski (2014): Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws. Ann. Probab. 42, no. 2, 497-526. To pdf file
#52: I. Nourdin and M.S. Taqqu (2014): Central and non-central limit theorems in a free probability setting. J. Theoret. Probab. 27, no. 1, 220-248. To pdf file
#51: 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, no. 2, 473-500. To pdf file
#50: I. Nourdin, G. Peccati and R. Speicher (2013): Multidimensional semicircular limits on the free Wigner chaos. Ascona Proceedings 2011, Progress in Probability 67, 211-221. To pdf file
#49: A. Deya and I. Nourdin (2012): Convergence of Wigner integrals to the tetilla law. ALEA 9, 101-127. To pdf file
#48: I. Nourdin and G. Peccati (2013): Poisson approximations on the free Wigner chaos. Ann. Probab. 41, no. 4, 2709-2723. To pdf file
#47: K. Es-Sebaiy and I. Nourdin (2013): Parameter estimation for alpha-fractional bridges. Malliavin Calculus and Stochastic Analysis, Springer Proceedings in Mathematics and Statistics34, 385-412. To pdf file
#46: I. Nourdin (2011): Yet another proof of the Nualart-Peccati criterion. Electron. Comm. Probab. 16, 467-481. To pdf file
#45: T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012): Wigner chaos and the fourth moment. Ann. Probab. 40, no. 4, 1577-1635. To pdf file
#44: S. Noreddine, I. Nourdin (2011): On the Gaussian approximation of vector-valued multiple integrals. J. Multiv. Anal. 102, no. 6, 1008-1017. To pdf file
#43: I. Nourdin, A. Réveillac and J. Swanson (2010): The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. Electron. J. Probab. 15, 2117-2162. To pdf file
#42: I. Nourdin, G. Peccati and M. Podolskij (2011): Quantitative Breuer-Major Theorems. Stoch. Proc. Appl. 121, no. 4, 793-812. To pdf file
#41: I. Nourdin and G. Peccati (2010): Cumulants on the Wiener Space. J. Funct. Anal. 258, 3775-3791. To pdf file
#40: 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. To pdf file
#39: I. Nourdin and G. Peccati (2009): Stein's method meets Malliavin calculus: a short survey with new estimates. In: Recent Development in Stochastic Dynamics and Stochastic Analysis, J. Duan, S. Luo and C. Wang editors, World Scientific. To pdf file
#38: B. Bercu, I. Nourdin and M.S. Taqqu (2010): Almost sure central limit theorems on the Wiener space. Stoch. Proc. Appl. 120, 1607-1628. To pdf file
#37: 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. To pdf file
#36: I. Nourdin, G. Peccati and G. Reinert (2010): Invariance principles for homogeneous sums: universality of Wiener chaos. Ann. Probab. 38, no. 5, 1947-1985. To pdf file
#35: 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. To pdf file
#34: X. Bardina, I. Nourdin, C. Rovira and S. Tindel (2010): Weak approximation of a fractional SDE. Stoch. Proc. Appl. 120, 39-65. To pdf file
#33: I. Nourdin, G. Peccati and G. Reinert (2009): Second order Poincaré inequalities and CLTs on Wiener space. J. Funct. Anal. 257, 593-609. To pdf file [This downloadable version has a couple of typos corrected with respect to the published version]
#32: I. Nourdin, G. Peccati and G. Reinert (2010): Stein's method and stochastic analysis for Rademacher functionals. Electron. J. Probab. 15, 1703-1742. To pdf file
#31: I. Nourdin and F.G. Viens (2009): Density formula and concentration inequalities with Malliavin calculus. Electron. J. Probab. 14, 2287-2309. To pdf file
#30: 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, 2304-2320. To pdf file
#29: J.-C. Breton and I. Nourdin (2008): Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion. Electron. Comm. Probab. 13, 482-493. To pdf file
#28: I. Nourdin, G. Peccati and A. Réveillac (2010): Multivariate normal approximation using Stein's method and Malliavin calculus. Ann. Inst. H. Poincaré Probab. Statist. 46, no. 1, 45-58. To pdf file
#27: I. Nourdin and G. Peccati (2009): Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields. Ann. Probab. 37, no. 6, 2231-2261. To pdf file
#26: 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. To pdf file
#25: I. Nourdin and G. Peccati (2009): Stein's method on Wiener chaos. Probab. Theory Related Fields 145, no. 1, 75-118. To pdf file
#24: A. Neuenkirch, I. Nourdin and S. Tindel (2008): Delay equations driven by rough paths. Electron. J. Probab. 13, 2031-2068. To pdf file
#23: I. Nourdin and G. Peccati (2008): Weighted power variations of iterated Brownian motion. Electron. J. Probab. 13, 1229-1256. To pdf file
#22: I. Nourdin, D. Nualart and C.A. Tudor (2010): Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Ann. Inst. H. Poincaré Probab. Statist.46, no. 4, 1055-1079. To pdf file
#21: I. Nourdin and G. Peccati (2009): Non-central convergence of multiple integrals. Ann. Probab. 37, no. 4, 1412-1426. To pdf file
#20: I. Nourdin and D. Nualart (2010): Central limit theorems for multiple Skorohod integrals. J. Theoret. Probab. 23, no. 1, 39-64. To pdf file
#19: I. Nourdin (2008): Asymptotic behavior of certain weighted quadratic and cubic variations of fractional Brownian motion. Ann. Probab. 36, no. 6, 2159-2175. To pdf file
#18: S. Darses and I. Nourdin (2008): Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2. Bernoulli 14, no. 3, 822-837. To pdf file
#17: M. Gradinaru and I. Nourdin (2009): Milstein's type schemes for fractional SDEs. Ann. Inst. H. Poincar\'e Probab. Statist. 45, no. 4, 1085-1098. To pdf file
#16: S. Darses, I. Nourdin and G. Peccati (2009): Differentiating sigma-fields for Gaussian and shifted Gaussian processes. Stochastics 81, no. 1, 79-97. To pdf file
#15: S. Darses and I. Nourdin (2007): Dynamical properties and characterization of gradient drift diffusions. Electron. Comm. Probab. 12, 390-400. To pdf file
#14: A. Neuenkirch, I. Nourdin, A. Rössler and S. Tindel (2009): Trees and asymptotic developments for fractional stochastic differential equations. Ann. Inst. H. Poincaré Probab. Statist. 45, no. 1, 157-174. To pdf file [You may prefer the extended version available here]
#13: L. Mazliak and I. Nourdin (2008): Optimal control for rough differential equations. Stoch. Dyn. 8 (special issue dedicated to Ludwig Arnold), no. 1, 23-33. To pdf file
#12: S. Darses and I. Nourdin (2007): Stochastic derivatives for fractional diffusions. Ann. Probab. 35, no. 5, 1998-2020. To pdf file
#11: I. Nourdin and T. Simon (2007): Correcting Newton-Cotes integrals by Lévy areas. Bernoulli 13, no. 3, 695-711. To pdf file
#10: A. Neuenkirch and I. Nourdin (2007): Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. J. Theoret. Probab. 20, no. 4, 871-899. To pdf file
#9: I. Nourdin and C.A. Tudor (2006): Some linear fractional stochastic equations. Stochastics 78, no. 2, 51-65. To pdf file
#8: I. Nourdin (2008): A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one. Sém. Probab. XLI, 181-197. To pdf file
#7: I. Nourdin and T. Simon (2006): On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion. Statist. Probab. Lett. 76, no. 9, 907-912. To pdf file
#6: M. Gradinaru, I. Nourdin and S. Tindel (2005): Itô's and Tanaka's type formulae for the stochastic heat equation: the linear case. J. Funct. Anal. 228, no. 1, 114-143. To pdf file
#5: I. Nourdin and T. Simon (2006): On the absolute continuity of Lévy processes with drift. Ann. Probab. 34, no. 3, 1035-1051. To pdf file
#4: M. Gradinaru and I. Nourdin (2008): Stochastic volatility: approximation and goodness-of-fit test. Probab. Math. Statist. 28, no. 1, 1-19. To pdf file
#3: I. Nourdin (2005): Schémas d'approximation associés à une équation différentielle dirigée par une fonction höldérienne; cas du mouvement brownien fractionnaire. C.R. Acad. Sci. Paris, Ser. I 340, no. 8, 611-614. To pdf file
#2: M. Gradinaru, I. Nourdin, F. Russo and P. Vallois (2005): m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index. Ann. Inst. H. Poincaré Probab. Statist. 41, no. 4, 781-806. To pdf file
#1: M. Gradinaru and I. Nourdin (2003): Approximation at first and second order of m-order integrals of the fractional Brownian motion and of certain semimartingales. Electron. J. Probab. 8, no. 18, 1-26. To pdf file