ABSTRACT
This chapter considers some problems concerning the asymptotic properties of stochastic evolution solutions, such as boundedness, asymptotic stability, invariant measures and small random perturbations. It introduces generalized Itô’s formula and the Lyapunov functional. By means of the Lya-punov functionals, the boundedness of solutions and the asymptotic stability of the null solution to some stochastic evolution equations are treated. The chapter examines the question on the existence of invariant measures and explores the small random perturbation problems. Finally, it briefly discusses the large deviations problem.
