Nonuniform stability in mean-square for stochastic differential equations in Hilbert spaces

Abstract

In this paper we study the relation between the nonuniform stability in mean square and admissibility of stochastic differential equation in Hilbert spaces. We consider an adapted norms and thus we obtain a variant for the stochastic case of nonuniform exponential stability in mean square due to in deterministic case. In the qualitative theory of evolution equations, nonuniform exponential stability is one the most important asymptotic properties and in last years it was treated from various perspectives The main objective is to give a more general concept of nonuniform exponential stability in mean square of stochastic differential equations in Hilbert spaces.