Abstract
It is shown that the transition semigroup $(P_t)_{t\geq0}$ corresponding to a nonlinear stochastic evolution equation is strong Feller and irreducible, provided the nonlinearities are Lipschitz continuous and the diffusion term is nondegenerate. This result ensures the uniqueness of the invariant measure for $(P_t)_{t\geq0}$.
Citation
Szymon Peszat. Jerzy Zabczyk. "Strong Feller Property and Irreducibility for Diffusions on Hilbert Spaces." Ann. Probab. 23 (1) 157 - 172, January, 1995. https://doi.org/10.1214/aop/1176988381
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