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

Markus C. Kunze
2012 Stochastics: An International Journal of Probability and Stochastic Processes  
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
more » ... variant measures for the associated transition semigroup.
doi:10.1080/17442508.2012.712973 fatcat:hbyya7i3nrapblmeb2shmywk4i