On the differentiability of solutions to singularly perturbed SPDEs

Abstract

We consider semilinear stochastic evolution equations on Hilbert spaces with multiplicative Wiener noise and linear drift term of the type $A+\epsilon G$, with $A$ and $G$ maximal monotone operators and $\epsilon$ a "small" parameter, and study the differentiability of mild solutions with respect to $\epsilon$. The operator $G$ can be a singular perturbation of $A$, in the sense that its domain can be strictly contained in the domain of $A$.

11 pages