Preprint no. 132
Mathematical Institute of the Academy of Sciences of the Czech Republic

Probabilistic approach to the strong Feller property

Bohdan Maslowski, Jan Seidler

Bohdan Maslowski, Mathematical Institute, Academy of Sciences,  Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: maslow@math.cas.cz; 
Jan Seidler, Mathematical Institute, Academy of Sciences,  Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: seidler@math.cas.cz, http://www.math.cas.cz/~seidler/

Summary: A new probabilistic method, based on the Girsanov theorem, for establishing the strong Feller property of diffusion processes in both finite and infinite dimensional spaces is proposed. Applications to second order stochastic differential equations, stochastic delay equations and stochastic partial differential equations of parabolic type are discussed, with a twofold aim: both to extend some older results, usually by weakening the assumptions on the drift term, and to obtain simpler proofs of them.

Mathematics Subject Classification (1991): 60J35, 60H15, 60H10, 60J60

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