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Strong Feller property for semilinear stochastic evolution equations and applications. (English) Zbl 0686.60053

Stochastic systems and optimization, Proc. 6th IFIP WG 7.1 Work. Conf., Warsaw/Pol. 1988, Lect. Notes Control Inf. Sci. 136, 210-224 (1989).
[For the entire collection see Zbl 0682.00016.]
The strong Feller property is proved for a stochastic evolution equation with a nonlinearity of the potential type in the drift term and a cylindrical white noise in the diffusion term. As consequences the strong law of large numbers and the uniqueness of an invariant measure are obtained. The results are applied to a stochastic reaction-diffusion equation with polynomial nonlinearity.
Reviewer: B.Maslowski

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Citations:

Zbl 0682.00016