On the small time asymptotics of diffusion processes on Hilbert spaces

Annals of Probability

Volumn 28, Issue 2, 2000, Pages 537-557

  Zhang, T S ^a,b  

^a Faculty of Science   (Norway)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Dirichlet form; Girsanov transform; Intrinsic metric; Large deviation; Stochastic evolution equation

Indexed keywords

EID: 0034345577     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1019160252     Document Type: Article

References (24)

1. AIDA, S. and KAWABI, X. (1999). Short time asymptotics of certain infinite dimensional diffusion processes. Preprint.
2. AIDA, S. and SHIGEKAWA, I. (1994). Logarithmic Sobolev inequalities and spectral gaps: perturbation theory. J. Funct. Anal. 448-475.
3. ALBEVERIO, S. and RÖCKNER, M. (1991). Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Probab. Theory Related Fields 89 347-386.
4. ALBEVERIO, S., RÖCKNER, M. and ZHANG, T. S. (1993). Girsanov transform for symmetric diffusions with infinite dimensional state space. Ann. Probab. 21 961-978.
5. BOGACHEV, V. I. and RÖCKNER, M. (1999). Mehler formula and capacities for infinite dimensional Ornstein-Uhlenbeck processes with general linear drift. Osaka Math. J. To appear.
6. CHOW, P. L. and MENALDI, J. L. (1990). Exponential estimates in exit probability for some diffusion processes in Hilbert spaces, Stochastics Stochastics Rep. 29 377-393.
7. DA PRATO, G. and ZABCZYK, J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press.
8. DAVIES, E. B. (1989). Heat Kernels and Spectral Theory. Cambridge Univ. Press.
9. DEMBO, A. and ZEITOUNI, O. (1993). Large Deviations Techniques. Jones and Bartlett, Boston.
10. FANG, S. (1994). On the Ornstein-Uhlenbeck process. Stochastics Stochastics Rep. 46 141-159.
11. FANG, S. and ZHANG, T. S. (1997). On the small time behavior of Ornstein-Uhlenbeck processes with unbounded linear drifts. Preprint. Probab. Theory Related Fields. To appear.
12. FUKUSHIMA, M. OSHIMA, Y. and TAKEDA, M. (1994). Dirichlet Forms and Symmetric Markov Processes. de Gruyter, Berlin.
13. 2-valued Ornstein-Uhlenbeck processes. Ann. Probab. 17 58-73.
14. KUO, H. H. (1977). Gaussian Measures in Banach Spaces. Lecture Notes in Math. Springer, Berlin.
15. LYONS, T. J. and ZHANG, T. S. (1994). Decomposition of Dirichlet processes and its applications. Ann. Probab. 22 494-524.
16. LYONS, T. J. and ZHENG, W. A. (1988). A crossing estimate for the canonical process on a Dirichlet space and tightness result. Colloque Paul Lévy sur les processes stochastique. Asterisque 157-158 248-272.
17. MA, Z. M. and RÖCKNER, M. (1992). An Introduction to the Theory of (Non-symmetric) Dirichlet Forms. Springer, Berlin.
18. PARDOUX, E. (1979). Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3 127-167.
19. RÖCKNER, M. and ZHANG, T. S. (1992). Uniqueness of generalized Schrödinger operators and applications. J. Funct. Anal. 105 187-231.
20. RÖCKNER, M. and ZHANG, T. S. (1994). Uniqueness of generalized Schrödinger operators II. J. Funct. Anal. 119 455-467.
21. STROOCK, D. (1984). An Introduction to the Theory of Large Deviations. Springer, Berlin.
22. TAKEDA, M. (1989). On a martingale method for symmetric diffusion processes and its applications. Osaka J. Math. 26 605-625.
23. TESSITORE, G. and ZABCZYK, J. (1998). Strict positivity for stochastic heat equations. Stochastic Process. Appl. 77 83-98.
24. VARADHAN, S. R. S. (1967). Diffusion processes in small time intervals. Comm. Pure Appl. Math. 20 659-685.