Abstract.
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.
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Received: 13 December 1999 / Published online: 5 September 2000
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Maslowski, B., Seidler, J. Probabilistic approach to the strong Feller property. Probab Theory Relat Fields 118, 187–210 (2000). https://doi.org/10.1007/s440-000-8014-0
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DOI: https://doi.org/10.1007/s440-000-8014-0
Keywords
- Differential Equation
- Partial Differential Equation
- Diffusion Process
- Dimensional Space
- Stochastic Differential Equation