Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities

Journal of Theoretical Probability

Volumn 10, Issue 4, 1997, Pages 835-848

  Hu, Yaozhong ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

Gaussian measure; Wiener process

Indexed keywords

EID: 0031478930     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022654314791     Document Type: Article

References (17)

1. Bakry D., and Emery M. (1985), Diffusions hypercontractives, Springer-Verlag, Sem. Prob. XIV, Lecture Notes in Mathematics 1123, 177-206.
2. Bakry D., and Michel D. (1992). Sur les inégalités FKG, Springer-Verlag, Sem. Prob. XXVI, Lecture Notes in Mathematics 1526, 170-188.
3. d, Math. Ann. 256, 569-575.
4. Bouleau N, and Lépingle, D. (1994). Numerical methods for Stochastic Processes, John Wiley and Sons Inc.
5. Dellacherie C., Meyer, P. A., and Maisonneuve, B. (1992). Probabilités et Potentiel, Vol. 5.
6. Fernández, R., Frölich, J., and Sokal, A. D. (1992). Random Walks, Critical Phenomena, and triviality in Quantum Field Theory, Springer.
7. Glimm, J., and Jaffe, A. (1987). Quantum Physics, A Functional Integral Point of View, Sec. Edition, Springer.
8. 2-expansion via iterated gradients: Ornstein-Uhlenbeck semigroup and entropy, Preprint.
9. Houdré, C., and Kagan, A. (1995). Variance inequalities for functions of Gaussian variables, J. Theor. Prob. 8, 23-30.
10. Houdré, C., and Pérez-Abreu, V. (1995). Covariance identities and inequalities for functional on Wiener space and Poisson space, Ann. Prob. 23, 400-419.
11. Hu, Y. Z., and Meyer, P. A. (1988). Chaos de Wiener et intégrales de Feynman, Springer, Sem. Prob. XXIII, Lecture Notes in Mathematics 1321, 51-71.
12. Isobe, E., and Sato, Sh. (1983). Wiener-Hermite expansion of a process generated by an Itô stochastic differential equation, J. Appl. Prob. 20, 754-765.
13. Itô, K. (1951). Multiple Wiener integrals, J. Math. Soc. Japan 3, 157-169.
14. Ledoux, M. (1993). L'algèbre de Lie des gradients itérés d'un générateur Markovien, C. R. 317, 1049-1052.
15. Ledoux, M. (1995). L'algèbre de Lie des gradients itérés d'un générateur Markovien -Développements de moyennes et entropies, Ann. Sci. Ecole Norm. Sup. 28, 435-460.
16. Pitt, L. D. (1977). A Gaussian correlation inequality for symmetric convex sets, Ann. Prob. 5, 470-474.
17. Sugita, H. (1992). Various topologies in the Wiener space and Levy stochastic area, Prob. Th. Rel. Fields 91, 283-296.