A class of stochastic evolution equations with additive noise (compensated Poisson random measures) in Hilbert spaces is considered. We first show existence and uniqueness of a mild solution to the stochastic equation with Lipschitz type coefficients. The properties (homogeneity, Markov, and Feller) of the solution are studied. We then study the stability and exponential ultimate boundedness properties of the solution by using Lyapunov function technique. We also study the conditions for the existence and uniqueness of an invariant measure associated to the solution. At last, an example is given to illustrate the theory.
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