Almost sure weak exponential stability with a certain decay function of semilinear stochastic evolutionequations

In this paper the weak exponential stability with decay function of sample path, which are given by mild solution to a class of semilinear stochastic evolution equations, are presented. The analyses consist in using exponential martingale formula, Lyapunov functional and some special inequalities derived for our stability purposes. Two examples are given to illustrate the theory.