Stochastic evolution equations with a spatially homogeneous Wiener process

Stochastic Processes and their Applications

Volumn 72, Issue 2, 1997, Pages 187-204

  Peszat, Szymon ^a   Zabczyk, Jerzy ^a  

^a INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Homogeneous Wiener process; Large deviation principle; Random environment; Stochastic partial differential equations

Indexed keywords

EID: 0031574567     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00089-6     Document Type: Article

References (31)

1. Bojdecki, T., Jakubowski, J., 1989. Ito stochastic integral in the dual of a nuclear space. J. Multivariate Anal. 31, 40-58.
2. Brzeźniak, Z., Peszat, S., 1997. Space-time continuous solutions to SPDEs driven by a homogeneous Wiener process. Preprint, School of Math., University of Hull.
3. Brzeźniak, Z., Peszat, S., Stochastic two dimensional Euler equations, in preparation.
4. Capiński, M., Peszat, S., On the existence of a solution to stochastic Navier-Stokes equations, in preparation.
5. Carmona, R., Molchanov, S.A., 1994. Parabolic Anderson problem and intermittency. Memoirs Amer. Math. Soc. 108, 1-125.
6. Da Prato, G., Zabczyk, J., 1992. Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press, Cambridge.
7. Da Prato, G., Zabczyk, J., 1995. Convergence to equilibrium for classical and quantum spin systems. Probab. Theory Related Fields 103, 529-552.
8. Da Prato, G., Zabczyk, J., 1996. Ergodicity for Infinite Dimensional Systems. Cambridge Univ. Press, Cambridge.
9. Davies, E.B., 1989. Heat Kernels and Spectral Theory. Cambridge Univ. Press, Cambridge.
10. Dawson, D.A., Salehi, H., Spatially homogeneous random evolutions. J. Multivariate Anal. 10, 141-180.
11. Eidel'man, S.D., 1969. Parabolic Systems. North-Holland, Groningen, Amsterdam.
12. Funaki, T., 1991. Regularity properties for stochastic partial differential equations of parabolic type. Osaka J. Math. 28, 495-516.
13. Gel'fand, I.M., Vilenkin, N.Ya., 1964. Generalized Functions. Vol. IV: Applications of Harmonic Analysis. Academic Press, New York.
14. Handa, K., 1996. On stochastic PDE related to Burgers' equation with noise, Collection: Nonlinear Stochastic PDES, Minneapolis, MN, 1994, IMA vol. Math. Appl. 77. Springer, New York, pp. 147-156.
15. Hida, T., Streit, L., 1977. On quantum theory in terms of white noise. Nagoya Math. J. 68, 21-34.
16. Holley, R.A., Stroock, D.W., 1978. Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motion. Publ. RIMS Kyoto Univ. 14, 741-788.
17. Itô, K., 1984. Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. SIAM, Philadelphia.
18. Kifer, Yu., 1995. The Burgers equation with a random force and a general model for directed polymers in random environments. Preprint.
19. Kotelenez, P., 1992. Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations. Stochastics Stochastics Rep. 41, 177-199.
20. Metivier, M., 1982. Semimartingales: A Course on Stochastic Processes. de Gruyer, Berlin.
21. Metivier, M., 1988. Stochastic Partial Differential Equations in Infinite Dimensional Spaces. Scuola Normale Superiore, Pisa.
22. Nobel, J., 1997. Evolution equation with Gaussian potential. Nonlinear Analysis: Theory Methods Appl. 28, 103-135.
23. Peszat, S., 1994. Large deviation principle for stochastic evolution equations. Probab. Theory Related Fields 98, 113-136.
24. Peszat, S., 1995. Existence and uniqueness of the solution for stochastic equations on Banach spaces. Stochastics Stochastics Rep. 55, 167-193.
25. Peszat, S., Zabczyk, J., 1995a. Strong Feller property and irreducibility for diffusions on Hubert spaces. Ann. Probab. 23, 157-172.
26. Peszat, S., Zabczyk, J., 1995b. Stochastic evolution equations with a spatially homogeneous Wiener process. Preprint 24, Scuola Normale Superiore, Pisa.
27. 2 Euclidean (Quantum) Field Theory. Princeton Univ. Press, Princeton.
28. Tessitore, G., Zabczyk, J., 1996a. Invariant measures for stochastic heat equations. Preprint 561, Institute of Math., Polish Acad. Sci., Warsaw.
29. Tessitore, G., Zabczyk, J., 1996b. Strong positivity for stochastic heat equations. Preprint 561, Institute of Math., Polish Acad. Sci., Warsaw.
30. Walsh, J.B., 1986. An introduction to stochastic partial differential equations, in: École d'été de probabilités de Saint-Flour XIV - 1984, Lecture Notes Math., vol. 1180. Springer, Berlin, pp. 265-439.
31. Zabczyk, J., 1993. The fractional calculus and stochastic evolution equations, in: Barcelona Seminar on Stochastic Analysis, St. Feliu de Guixol 1991. Birkhäuser, Basel, Boston, pp. 222-234.