Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces

Details Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces

2011-01-12

arxiv.org/abs/1101.2369v1

Mathematics

Probability

24 pages, no figures

Scientific paper

We prove a Miyadera-Voigt type perturbation theorem for strong Feller semigroups. Using this result, we prove well-posedness of the semilinear stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable Banach space E, assuming that F is bounded and measurable and that the associated linear equation, i.e.\ the equation with F = 0, is well-posed and its transition semigroup is strongly Feller and satisfies an appropriate gradient estimate. We also study existence and uniqueness of invariant measures for the associated transition semigroup and discuss extensions of our results to nonlinearities F which are unbounded.

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