ABSTRACT
In this paper we shall give an expository survey on the topic of asymptotic stability of stochastic evolution equations in Hilbert spaces. The study of these kinds of equations is motivated by the internal developments of analysis and the theory of stochastic processes such as stochastic partial differential equations and stochastic delay differential equations on one side, and by a need to describe random phenomena studied in natural sciences like chemistry, biology and in control theory, on the other. In particular, we shall content ourselves with the presentation of some recent progress made by various probabilists and authors, including ourselves over the last several years.
