Cumulants on the Wiener space

Journal of Functional Analysis

Volumn 258, Issue 11, 2010, Pages 3775-3791

  Nourdin, Ivan ^a   Peccati, Giovanni ^a,b  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Cumulants; Diagram formulae; Gaussian processes; Malliavin calculus; Ornstein Uhlenbeck semigroup

Indexed keywords

EID: 77949568795     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.10.024     Document Type: Article

References (26)

1. Airault H., Malliavin P., and Viens F.G. Stokes formula on the Wiener space and n-dimensional Nourdin-Peccati analysis. J. Funct. Anal. 258 5 (2010) 1763-1783
2. Barbour A.D. Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Theory Related Fields 72 2 (1986) 289-303
3. Breton J.-C., Nourdin I., and Peccati G. Exact confidence intervals for the Hurst parameter of a fractional Brownian motion. Electron. J. Stat. 3 (2009) 416-425 (electronic)
4. Breuer P., and Major P. Central limit theorems for non-linear functionals of Gaussian fields. J. Multivariate Anal. 13 (1983) 425-441
5. Chambers D., and Slud E. Central limit theorems for nonlinear functionals of stationary Gaussian processes. Probab. Theory Related Fields 80 (1989) 323-349
6. Chen L.H.Y., and Shao Q.-M. Stein's method for normal approximation. In: Barbour A.D., and Chen L.H.Y. (Eds). An Introduction to Stein's Method. Lecture Notes Ser. vol. 4 (2005), Institute for Mathematical Sciences, National University of Singapore, Singapore University Press, World Scientific 1-59
7. Fox R., and Taqqu M.S. Multiple stochastic integrals with dependent integrators. J. Multivariate Anal. 21 1 (1987) 105-127
8. Giraitis L., and Surgailis D. CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrsch. Verw. Gebiete 70 (1985) 191-212
9. Janson S. Gaussian Hilbert Spaces (1997), Cambridge University Press, Cambridge
10. Malliavin P. Stochastic Analysis (1997), Springer-Verlag, Berlin, Heidelberg, New York
11. Marinucci D. A central limit theorem and higher order results for the angular bispectrum. Probab. Theory Related Fields 141 (2007) 389-409
12. Nourdin I., and Peccati G. Non-central convergence of multiple integrals. Ann. Probab. 37 4 (2007) 1412-1426
13. Nourdin I., and Peccati G. Stein's method on Wiener chaos. Probab. Theory Related Fields 145 1 (2009) 75-118
14. I. Nourdin, G. Peccati, Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields, Ann. Probab. (2009), in press
15. I. Nourdin, G. Peccati, Universal Gaussian fluctuations of non-Hermitian matrix ensembles, preprint, 2008
16. Nourdin I., Peccati G., and Reinert G. Second order Poincaré inequalities and CLTs on Wiener space. J. Func. Anal. 257 (2009) 593-609
17. I. Nourdin, G. Peccati, G. Reinert, Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos, preprint, 2009
18. I. Nourdin, G. Peccati, A. Réveillac, Multivariate normal approximation using Stein's method and Malliavin calculus, Ann. Inst. H. Poincaré Probab. Statist. (2009), in press
19. Nourdin I., and Viens F.G. Density estimates and concentration inequalities with Malliavin calculus. Electron. J. Probab. 14 (2009) 2287-2309
20. Nualart D. The Malliavin calculus and related topics of Probability and Its Applications (2006), Springer-Verlag, Berlin
21. Nualart D., and Ortiz-Latorre S. Central limit theorems for multiple stochastic integrals and Malliavin calculus. Stochastic Process. Appl. 118 4 (2008) 614-628
22. Nualart D., and Peccati G. Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 1 (2005) 177-193
23. G. Peccati, M.S. Taqqu, Moments, cumulants and diagram formulae for non-linear functionals of random measures (survey), preprint, 2008
24. Peccati G., and Tudor C.A. Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII. Lecture Notes in Math. vol. 1857 (2005), Springer-Verlag, Berlin, Heidelberg, New York 247-262
25. Reinert G. Three general approaches to Stein's method. In: Barbour A.D., and Chen L.H.Y. (Eds). An Introduction to Stein's Method. Lecture Notes Ser. vol. 4 (2005), Institute for Mathematical Sciences, National University of Singapore, Singapore University Press, World Scientific 183-221
26. Rotar' V. Stein's method, Edeworth's expansions and a formula of Barbour. In: Barbour A.D., and Chen L.H.Y. (Eds). An Introduction to Stein's Method. Lecture Notes Ser. vol. 4 (2005), Institute for Mathematical Sciences, National University of Singapore, Singapore University Press, World Scientific 59-84