Stability with a general rate function for a class of stochastic evolution equations in infinite dimensional spaces

The aim of this paper is to investigate the almost sure stability with a certain rate function lambda(t) for a class of stochastic evolution equations in infinite dimensional spaces under various sufficient conditions. The results obtained here include exponential and polynomial stability as special cases. Much more refined sufficient conditions than the usual ones, for example, those described in [14], are obtained under our framework by the method of Liapunov functions. Two examples are given to illustrate our theory.