Stability properties in the $\alpha-$norm of solutions of stochastic partial functional differential equations

Abstract

In this paper, we study almost sure exponential stability and asymptotic stability in probability of mild solutions of stochastic partial functional differential equations in Hilbert spaces. The linear part is assumed to generate an analytic semigroup while the drift and diffusion terms satisfy a Hölder type condition with respect to the fractional power norm of the linear part.