On a class of stochastic equations in Hilbert spaces: Solvability and smoothing properties

Stochastic Analysis and Applications

Volumn 17, Issue 1, 1999, Pages 43-69

  Fuhrman, Marco ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039252800     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1080/07362999908809587     Document Type: Article

References (16)

1. G. Da Prato, D. Nualart and J. Zabczyk, Strong Feller property for infinite-dimensional stochastic equations, preprint Scuola Normale Superior di Pisa, 1994.
2. G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, 1992.
3. G. Da Prato and J. Zabczyk, Ergodicity for infinite dimensional systems, Cambridge University Press, 1996.
4. M. Fuhrman, Smoothing properties of transition semigroups in Hilbert spaces, Nonlinear Differential Equations Appl. 3 (1995), 445-464.
5. B. Gaveau and J.M. Moulinier, Régularité des mesures et perturbations stochastiques de champs de vecteurs sur des espaces de dimension infinie, Publ. RIMS Kyoto Univ. 21 (1985), 593-616.
6. G. Jona-Lasinio and R. Sénéor, Study of stochastic differential equations by constructive methods I, preprint.
7. J.M. Lasry and P.L. Lions, A remark on regularization in Hilbert spaces, Israel J. Math. 55 (3) (1986), 257-266.
8. B. Maslowski, On probability distributions of solutions of semilinear stochastic evolution equations, Stochastics Stochastics Rep. 45 (1993), 17-44.
9. A.S. Nernirovski and S.M. Semenov, The polynomial approximation of functions in Hubert spaces, Mat. Sb. (N.S) 92 (1973), 134, 257-281.
10. D. Nualart, The Malliavin calculus and related topics, Springer Verlag, 1995.
11. S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Ann. Prob. 23 (1) (1995), 157-172.
12. M. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol I: Functional Analysis, Academic Press, 1975.
13. I. Shigekawa, Existence of invariant measures of diffusions on an abstract Wiener space, Osaka J. Math. 24 (1987), 37-59.
14. I. Simão, Regular fundamental solution for a parabolic equation on an infinite-dimensional space, Stochastic Anal. Appl. 11 (1993), 235-247.
15. I. Simão, Regular transition densities for infinite dimensional diffusions, Stochastic Anal. Appl. 11 (1993), 309-336.
16. J. Zabczyk, Mathematical control theory: an introduction, Birkäuser, 1992.