Multi-dimensional Gaussian fluctuations on the poisson space

Electronic Journal of Probability

Volumn 15, Issue , 2010, Pages 1487-1527

  Peccati, Giovanni ^a   Zheng, Cengbo ^b,c  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

Central Limit Theorems; Malliavin calculus; Multi dimensional normal approximations; Ornstein Uhlenbeck processes; Poisson measures; Probabilistic Interpolations; Stein s method

Indexed keywords

EID: 78649701667     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v15-813     Document Type: Article

References (26)

1. A. D. Barbour. Stein's method for diffusion approximations. Probab. Theory Related Fields, 84(3):297-322, 2008.
2. O.E. Barndorff-Nielsen and N. Shephard. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. R. Statist. Soc. B,63(2):167-241, 2001.
3. P De Blasi, G. Peccati, and I. Prünster. Asymptotics for posterior hazards. Ann. Statist., 37(4):1906-1945, 2009.
4. S. Chatterjee. Chaos, concentration, and multiple valleys. Preprint, 2009.
5. S. Chatterjee and E. Meckes. Multivariate normal approximation using exchangeable pairs. Preprint, 2007.
6. F. Gotze. On the rate of convergence in the multivariate clt. Ann. Probab., 19(2):724-739, 1991.
7. Y. Kabanov. On extended stochastic integrals. Theor. Probab. Appl, 20:710-722, 1975.
8. P Malliavin. Stochastic Analysis. Springer-Verlag, Berlin, Heidlelberg, New York, 1997.
9. I. Nourdin and G. Peccati. Stein's method on Wiener chaos. Prob. Theory Related Fields, 145(1-2):75-118, 2009.
10. I. Nourdin, G. Peccati, and G. Reinert. Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos. Ann. Probab., 2010, in press.
11. I. Nourdin, G. Peccati, and A. Réveillac. Multivariate normal approximation using Stein's method and Malliavin calculus. Ann. Inst. H. Poincaré Probab. Statist.,46(1):45-58, 2010.
12. D. Nualart. The Malliavin calculus and related topics (2nd edition). Springer-Verlag, Berlin, 2006.
13. D. Nualart and S. Ortiz-Latorre. Central limit theorems for multiple stochastic integrals and Malliavin calculus. Stochastic Process. Appl., 118(4):614-628, 2008.
14. D. Nualart and G. Peccati. Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab., 33(1):177-193, 2005.
15. D. Nualart and J. Vives. Anticipative calculus for the Poisson process based on the Fock space. In Séminaire de Probabilités XXIV, pages 154-165. Springer, Berlin, 1990. LNM 1426.
16. G. Peccati and I. Prünster. Linear and quadratic functionals of random hazard rates: an asymptotic analysis. Ann. Appl. Probab., 18(5):1910-1943, 2008.
17. G. Peccati, J.L. Solé, M.S. Taqqu, and F Utzet. Stein's method and normal approximation of Poisson functionals. Ann. Probab., 38(2):443-478, 2010.
18. G. Peccati and M.S. Taqqu. Central limit theorems for double Poisson integrals. Bernoulli, 14(3):791-821, 2008.
19. G. Peccati and M.S. Taqqu. Wiener chaos: moments, cumulants and diagrams. A survey with computer implementation Bocconi & Springer Series. Spriinger-Verlag, Berlin, 2010.
20. G. Peccati and C.A. Tudor. Gaussian limits for vector-valued multiple stochastic integrals. In Séminaire de Probabilités XXXVIII, pages 247-262. Berlin, 2005.
21. J. Picard. Formules de dualités sur l'espace de Poisson. Ann. Inst. H. Poincaré B, 32(4):509-548, 1996.
22. N. Privault. Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales. Springer, Berlin, 2009.
23. G. Reinert and A. Rollin. Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition. Ann. Probab., 37(6):2150-2173, 2009.
24. D. Surgailis. On multiple Poisson stochastic integrals and associated Markov semigroups. Probab. Math. Stat., 3(2):217-239, 1984.
25. D. Surgailis. CLTs for polynomials of linear sequences: Diagram formulae with illustrations. In Theory and applications of long range dependence, pages 111-127. 2003.
26. M. Talagrand. Spin Glasses: a Challange for Mathematicians. Cavity and Mean fields. Springer, Berlin, 2003.