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Strong Feller property for stochastic semilinear equations. (English) Zbl 0817.60081
This short note deals with the regularity of the transition semigroup corresponding to the stochastic differential equation \(dX(t) = (AX + F(X))dt + dW(t)\). Strong Feller property is obtained when the equation is defined on an infinite-dimensional separable Hilbert space. One considers the cases when \(F(X)\) is a smooth nonlinearity and when it is a dissipative nonlinearity.

MSC:
60J35 Transition functions, generators and resolvents
47D07 Markov semigroups and applications to diffusion processes
60H99 Stochastic analysis
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