Existence of invariant measures for diffusion processes on a Wiener space

Osaka Journal of Mathematics

Volumn 35, Issue 3, 1998, Pages 717-734

  Hino, Masanori ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011375822     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. S. Albeverio and M. Röckner: Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms, Probab. Th. Rel. Fields, 89 (1991), 347-386.
2. V.I. Bogachev, N. Krylov and M. Röckner: Regularity of invariant measures: the case of non-constant diffusion part, J. Funct. Anal. 138 (1996), 223-242.
3. V.I. Bogachev and M. Röckner: Regularity of invariant measures on finite and infinite dimensional spaces and applications, J. Funct. Anal. 133 (1995), 168-223.
4. E.B. Davies: Heat Kernels and Spectral theory, Cambridge University Press, Cambridge, 1989.
5. J.-D. Deuschel and D.W. Stroock: Large Deviations, Academic Press, San Diego, 1989.
6. M. Fukushima, Y. Oshima, and M. Takeda: Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin-New York, 1994.
7. L. Gross: Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083.
8. L. Gross: Logarithmic Sobolev inequalities and contractivity properties of semigroups, Dirichlet Forms, eds. G. Dell'Antonio and U. Mosco, Lecture Notes in Math. 1563, 54-88, Springer-Verlag, Berlin-Heidelberg-New York, 1993.
9. M. Hino: Convergence of non-symmetric forms, to appear in J. Math. Kyoto Univ.
10. T. Kato: Perturbation Theory for Linear Operators, second ed., Springer-Verlag, Berlin-Heidelberg-New York, 1980.
11. T. Kazumi: Le processus d'Ornstein-Uhlenbeck sur l'espace des chemins riemanniens et le problème des martingales, J. Funct. Anal. 144 (1997), 20-45.
12. S. Kusuoka: Dirichlet forms and diffusion processes on Banach spaces, J. Fac. Sci. Univ. Tokyo, Sec. IA, 29 (1982), 79-95.
13. T. Lyons and T.S. Zhang: Convergence of non-symmetric Dirichlet processes, Stochastics S-tochastics Rep. 57 (1996), 159-167.
14. Z.M. Ma and M. Röckner: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, Berlin-Heidelberg-New York, 1992.
15. A. Pazy: Semigroups of Linear Operator and Application to Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1983.
16. M. Röckner and T.S. Zhang: Finite dimensional approximation of diffusion processes on infinite dimensional spaces, Stochastics Stochastics Rep. 57 (1996), 37-55.
17. I. Shigekawa: Existence of invariant measures of diffusions on an abstract Wiener space, Osaka J. Math. 24 (1987), 37-59.
18. p contraction semigroups for vector valued functions, J. Funct. Anal. 147 (1997), 69-108.
19. I. Shigekawa and S. Taniguchi: Dirichlet forms on separable metric spaces, Proceedings of the sixth USSR-Japan Symposium on Probability Theory and Mathematical Statistics, eds. A.N. Shiryaev, V.S. Korolyuk, S. Watanabe and M. Fukushima, 324-353, World Scientific, Singapore, 1992.
20. W. Stannat: First order perturbations of Dirichlet operators: existence and uniqueness, J. Funct. Anal. 141 (1996), 216-248.
21. R.v. Vintschger: The existence of invariant measures for C[0, 1]-valued diffusions, Probab. Th. Rel. Fields, 82 (1989), 307-313.
22. T.S. Zhang: Existence of invariant measures for diffusion processes with infinite dimensional state space, Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, R. Høegh-Krohn Memorial, I, 283-294, Cambridge Univ. Press, Cambridge, UK, 1992.