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 beautiful 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 (including research papers, slides of talks, lecture notes, etc.) having any link with the fourth moment theorem and related stuff.
Although my goal has been to be as comprehensive
as possible, several links are surely missing, so please feel free to contact me (inourdin@gmail.com) in case.
Year 2013
- E. Azmoodeh and J.I. Morlanes (2013): Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind, preprint
- E. Azmoodeh and L. Viitasaari (2013): Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind, preprint
- J.-M. Bardet and C.A. Tudor (2013): Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process, preprint
- A. Deya, D. Nualart and S. Tindel (2013): On L2 modulus of continuity of Brownian local times and Riesz potentials, preprint
- D. Harnett and D. Nualart (2013): On Simpson's rule and fractional Brownian motion with H = 1/10, preprint
- Y. Hu, F. Lu and D. Nualart (2013): Convergence of densities of some functionals of Gaussian processes, preprint
- 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
- I. Nourdin, D. Nualart and G. Peccati (2013): Quantitative stable limit theorems on the Wiener space, preprint
- I. Nourdin, G. Peccati and Y. Swan (2013): Entropy and the fourth moment phenomenon, preprint
- I. Nourdin and G. Peccati (2013): The optimal fourth moment theorem, preprint
- D. Nualart and J. Swanson (2013): Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II, preprint
- E. Nualart and F.G. Viens (2013): Hitting probabilities for general Gaussian processes, preprint
- M. S. Pakkanen (2013): Limit theorems for power variations of ambit fields driven by white noise, preprint
- G. Peccati and C. Thaele (2013): Gamma limits and U-statistics on the Poisson space, preprint
- V. H. Pham (2013): On the rate of convergence for central limit theorems of sojourn times of Gaussian fields, preprint
- C. A. Tudor (2013): The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals, preprint
Year 2012
- S. Aazizi (2012): A Simple Proof of Berry-Esséen Bounds for the Quadratic Variation of the Subfractional Brownian Motion. Preprint
- S. Aazizi and K. Es-Sebaiy (2012): Berry-Esseen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion. Preprint
- 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
- S. Bai and M. S. Taqqu (2012): Multivariate limit theorems in the context of long-range dependence. Preprint
- J.-M. Bardet and D. Surgailis (2012): Moment bounds and central limit theorems for Gaussian subordinated arrays, J. Multi. Anal., to appear
- 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
- 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
- S. Bourguin and G. Peccati (2012): Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering, preprint
- 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
- K. Burdzy, D. Nualart and J. Swanson (2012): Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion, preprint
- 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
- J.M. Corcuera, E. Hedevang, M.S. Pakkanen and M. Podolskij (2012): Asymptotic theory for Brownian semi-stationary processes with application to turbulence, preprint
- L. Decreusefond, E. Ferraz, P. Martins and T. Vu (2012): Robust methods for LTE and WiMAX dimensioning, Preprint
- A. Deya, S. Noreddine and I. Nourdin (2012): Fourth Moment Theorem and q-Brownian Chaos, Comm. Math. Phys., to appear.
- A. Deya and I. Nourdin (2012): Convergence of Wigner integrals to the tetilla law, ALEA 9, 101-127.
- C. Durastanti, X. Lan and D. Marinucci (2012): Needlet-Whittle Estimates on the Unit Sphere. Preprint.
- C. Durastanti, D. Marinucci and G. Peccati (2012): Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields. Preprint.
- R. Eden and J. Víquez (2012): Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions, Preprint
- K. Es-Sebaiy (2012): Berry-Esseen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes , Preprint
- D. Harnett and D. Nualart (2012): CLT for an iterated integral with respect to fBm with H>1/2, preprint
- J. Istas (2012): Estimating self-similarity through complex variations, Electron. J. Statist. 6, 1392-1408
- T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012): Wigner chaos and the fourth moment, Ann. Probab. 40, no. 4, 1577-1635.
- S. Kusuoka (2012): Survey on the fourth moment theorem, Stein's method and related topics, Tohoku University
- 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.
- R. Lachieze-Rey and G. Peccati (2012): Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics, preprint
- G. Last, M. D. Penrose, M. Schulte and C. Thaele (2012): Moments and central limit theorems for some multivariate Poisson functionals, preprint
- D. Marinucci and I. Wigman (2012): On Nonlinear Functionals of Random Spherical Eigenfunctions, preprint
- I. Nourdin (2012): Selected aspects of fractional Brownian motion, Springer Verlag (Bocconi and Springer Series), to appear.
- I. Nourdin (2012): Lectures on Gaussian approximations with Malliavin calculus, Prix de la Fondation des Sciences Mathématiques de Paris
- I. Nourdin (2012): Approximation gaussienne à l’aide du calcul de Malliavin: de la méthode de Stein à l’universalité, Cours de la Fondation des Sciences Mathématiques de Paris, January to March, Collège de France
- I. Nourdin, D. Nualart and G. Poly (2012): Absolute continuity and convergence of densities for random vectors on Wiener chaos, preprint
- I. Nourdin and G. Peccati (2012): Normal approximations with Malliavin calculus: from Stein's method to universality. Cambridge University Press (Cambridge Tracts in Mathematics)
- I. Nourdin and G. Poly (2012): Convergence in law in the second Wiener/Wigner chaos, Elect. Comm. in Probab. 17, no. 36.
- I. Nourdin and G. Poly (2012): Convergence in total variation on Wiener chaos, Stoch. Proc. Appl., to appear
- G. Peccati (2012): Stein's method meets Malliavin calculus, Brussels, Belgium
- J. Rosinski (2012): Asymptotic independence and limit laws for Wiener chaos, 6th International Conference on Stochastic Analysis and Its Applications, Bedlewo, Poland
- M. Schulte (2012): A Central Limit Theorem for the Poisson-Voronoi Approximation, Adv. Appl. Math. 49, no. 3-5, 285-306
- M. Schulte (2012): Normal approximation of Poisson functionals in Kolmogorov distance, preprint
- 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
- M. Schulte and C. Thaele (2012): Distances between Poisson k-flats, preprint
- J.J. Víquez (2012): Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions, Probability Seminar, February 2012, Purdue University, USA.
Year 2011
- O. Aboura and S. Bourguin (2011): Density estimates for solutions to one dimensional backward SDE's. Potential Analysis, to appear.
- O. E. Barndorff-Nielsen, J. M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semi-stationary processes, Bernoulli 17, no. 4, 1159-1194.
- 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
- A. Bonami (2011): Quantitative Central Limit Theorems, Conference ``Analysis 2011, in honor of Martine and Hervé Queffélec'', June 14-17, University of Lille 1
- S. Bourguin and C.A. Tudor (2011): Malliavin Calculus and Self Normalized Sums, Sém. Probab., in revision
- 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
- S. Bourguin and C.A. Tudor (2011): Cramér's theorem for Gamma random variables, Electron. Comm. Probab. 16, no. 1, 365-378.
- 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'')
- J.M. Corcuera (2011): New Central Limit Theorems for Functionals of Gaussian Processes and their Applications. Methodol. Comput. Appl. Probab. (online first)
- L. Decreusefond, E. Ferraz and H. Randriam (2011): Simplicial Homology of Random Configurations, Preprint
- A. Deya and I. Nourdin (2011): Invariance principles for homogeneous sums of free random variables, Bernoulli, to appear
- C. Durastanti, X. Lan and D. Marinucci (2011): Gaussian Semiparametric Estimates on the Unit Sphere, Bernoulli, to appear
- K. Es-Sebaiy and C. 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.
- E. Ferraz and A. Vergne (2011): Statistics of geometric random simplicial complexes, Preprint
- 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
- R. Lachieze-Rey and G. Peccati (2011): Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs, preprint
- F. Lu (2011): Malliavin Calculus, Its Applications to SPDE and Convergence in Density, oral comprehensive exam, October 19, University of Kansas
- 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.
- M.T. Nguyen (2011): Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes, preprint
- S. Noreddine and I. Nourdin (2011): On the Gaussian approximation of vector-valued multiple integrals, J. Multiv. Anal. 102, no. 6, 1008-1017.
- I. Nourdin (2011): Yet another proof of the Nualart-Peccati criterion, Electron. Comm. Probab. 16, 467-481
- I. Nourdin and G. Peccati (2011): Poisson approximations on the free Wigner chaos, Ann. Probab., to appear
- I. Nourdin, G. Peccati and M. Podolskij (2011): Quantitative Breuer-Major theorems. Stoch. Proc. Appl. 121, no. 4, 793-812.
- I. Nourdin, G. Peccati and R. Speicher (2011): Multidimensional semicircular limits on the free Wigner chaos, Ascona 2011 Proceedings, to appear
- I. Nourdin and J. Rosiński (2011): Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws, Ann. Probab., to appear
- I. Nourdin and M.S. Taqqu (2011): Central and non-central limit theorems in a free probability setting, J. Theoret. Probab., under revision.
- 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.
- 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
- G. Peccati (2011): The Chen-Stein method for Poisson functionals, Preprint
- G. Peccati and C. Zheng (2011): Universal Gaussian fluctuations on the discrete Poisson chaos, Preprint
- M. Reitzner and M. Schulte (2011): Central Limit Theorems for U-Statistics of Poisson Point Processes, Ann. Probab., to appear
- 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.
- C.A. Tudor (2011): Asymptotic Cramér's theorem and analysis on Wiener space, Séminaire de Probabilités XLIII, Lecture Notes in Mathematics, 309-325
- J.J. Víquez (2011): On the second order Poincaré inequality and CLT's on Wiener-Poisson space, Probability Seminar, April 2011, Purdue University, USA.
- J. Víquez (2011): On the second order Poincaré inequality and CLT on Wiener-Poisson space, Preprint
Year 2010
- 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
- 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
- V. Bogachev (2010): Differentiable Measures and the Malliavin Calculus, American Mathematical Society (see more precisely pages 321-323)
- 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
- R. Eden and F.G. Viens (2010): General upper and lower tail estimates using Malliavin calculus and Stein's equations, Preprint
- Y. Hu and D. Nualart (2010): Parameter estimation for fractional Ornstein-Uhlenbeck processes, Stat. Probab. Lett. 80, no. 11-12, 1030-1038
- M. Ledoux (2010): Chaos of a Markov operator and the fourth moment condition, Ann. Probab., to appear
- D. Marinucci and I. Wigman (2010): On the Excursion Sets of Spherical Gaussian Eigenfunctions, J. Math. Phys., to appear
- D. Marinucci and G. Peccati (2010): Ergodicity and Gaussianity for Spherical Random Fields, J. Math. Phys. 51, 043301
- 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.
- A. Neuenkirch, S. Tindel and J. Unterberger (2010): Discretizing the fractional Levy area, Stoch. Proc. Appl. 120, no. 2, 223-254
- I. Nourdin (2010): Convergence des intégrales multiples de Wigner vers la loi semi-circulaire, 50th anniversary of the Laboratoire de Probabilités et Modèles Aléatoires, December 6-7, University of Paris 6
- I. Nourdin and D. Nualart (2010): Central limit theorems for multiple Skorohod integrals, J. Theoret. Probab. 23, no. 1, 39-64
- 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
- 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
- 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
- I. Nourdin and G. Peccati (2010): Cumulants on the Wiener space, J. Funct. Anal. 258, 3775-3791
- 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
- 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
- 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
- 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
- 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.
- G. Peccati (2010): Stein's method and Malliavin calculus on the Poisson space, Workshop on Malliavin Calculus for Jump Processes, November 18-20, Université Paris-Est
- G. Peccati (2010): Universal Gaussian fluctuations on the Wiener chaos, Conference on Probability and Stochastic Processes, August 13-17, Indian Statistical Institute, Bangalore
- 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
- 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'')
- G. Peccati and C. Zheng (2010): Multi-dimensional Gaussian fluctuations on the Poisson space, Elect. J. Probab. 15, no. 48, 1487-1527
- M. Podolskij (2010): Asymptotic expansion for multiple integrals, International Conference Dynstoch Meeting, June 16-19, University of Angers
- A. Réveillac, M. Stauch and C.A. Tudor (2010): Hermite variations of the fractional Brownian sheet. Stoch. Dyn., to appear.
- A. Rohde and C. Strauch (2010): Malliavin-Kalkül und Steinsche Methode, Universität Hamburg
- M. Schulte and C. Thaele (2010): Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes, Preprint
- C.A. Tudor (2010): Hsu-Robbins theorem for the correlated sequences, Colloque Franco-Roumain de Mathématiques Appliquées, August 2010, Poitiers, France.
- F.G. Viens (2010): Application of Stein's lemma and Malliavin calculus to the densities and fluctuation exponents of stochastic heat equations, Conference on SPDEs, January 6th, Isaac Newton Institute for Mathematical Sciences
Year 2009
- P. Baldi, G. Kerkyacharian, D. Marinucci and D. Picard (2009): Asymptotics for spherical needlets, Ann. Statist. 37, no. 3, 1150-1171.
- 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
- 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
- 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
- B. Buchmann and N. H. Chan (2009): Integrated functionals of normal and fractional processes, Ann. Appl. Probab. 19, no. 1, 49-70.
- X. Lan and D. Marinucci (2009): On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields, Stoch. Proc. Appl. 119 3749-3766
- 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
- I. Nourdin and G. Peccati (2009): Non-central convergence of multiple integrals, Ann. Probab. 37, no. 4, 1412–1426
- I. Nourdin and G. Peccati (2009): Stein's method on Wiener chaos, Probab. Theory Rel. Fields 145, no. 1, 75-118
- I. Nourdin, G. Peccati and G. Reinert (2009): Second order Poincaré inequalities and CLTs on Wiener space, J. Funct. Anal. 257, 593-609
- 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
- I. Nourdin and F.G. Viens (2009): Density formula and concentration inequalities with Malliavin calculus, Electron. J. Probab. 14, 2287-2309
- 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'')
- 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.
- S. Ortiz-Latorre (2009): An introduction to Stein’s Method, Barcelona Probability Seminar
- G. Peccati (2009): Stein's method, Malliavin calculus and infinite-dimensional Gaussian analysis, Progress in Stein’s Method, Singapore
- G. Reinert (2009): Stein’s method and stochastic analysis of Rademacher functionals, Progress in Stein’s Method, January 12-16, National University of Singapore
- G. Reinert (2009): Gaussian approximation using Stein's method: from one to infinite dimensions and back, Symposium on probability theory in honor of Professor Andrew Barbour, December 4th, Universität Zürich
- G. Reinert (2009): Gaussian approximation of functionals: Malliavin calculus and Stein’s method, Proceedings of the 33rd Conference on Stochastic Processes and Their Applications, to appear
- 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
- 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
- C.A. Tudor (2009): Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion, Elect. Comm. in Probab. 14, 278–289
- 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
- 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
- X. Lan and D. Marinucci (2008): The needlets bispectrum, Electron. J. Statist. 2, 332-367
- 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
- I. Nourdin and G. Peccati (2008): Weighted power variations of iterated Brownian motion, Elect. J. Probab. 13, no. 43, 1229-1256
- 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
- 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
- G. Peccati (2007): Gaussian approximations of multiple integrals, Elect. Comm. in Probab. 12, 350-364
Year 2006
- 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
- Y. Hu and D. Nualart (2005): Renormalized self-intersection local time for fractional Brownian motion, Ann. Probab. 33, no. 3, 948-983
- D. Nualart and G. Peccati (2005): Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33, no. 1, 177-193
Year 2004
- G. Peccati and C.A. Tudor (2004): Gaussian limits for vector-valued multiple stochastic integrals, Séminaire de Probabilités XXXVIII, 247-262