Lyapunov functionals and asymptotic stability of stochastic delay evolution equations

The aim of this paper is to investigate the almost sure stability decay rate of mild solutions for a class of Hilbert space-valued stochastic delay evolution equations. To take advantage of the ideas from [14] for strong solutions to deal with the mild solution situation, the analysis is based on introducing an approximating system and using a limiting argument to deduce some properties of mild solutions. Several examples associated with stochastic partial differential equations are studied to illustrate our theory

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