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Semilinear stochastic evolution equations: Boundedness, stability and invariant measures. (English) Zbl 0538.60068
Semilinear stochastic evolution equations on a Hilbert space are studied. Properties covered include existence and uniqueness of solutions, the Markov and Feller properties, the continuity of sample paths, boundedness and stability of moments, stability of sample paths, and the existence and uniqueness of invariant measures. In addition, a more general version of Ito’s formula for mild solutions of stochastic evolution equations is established. Extensions to local Lipschitzian nonlinearities are also obtained and some examples of stochastic p.d.e’s and delay equations are discussed.
Reviewer: R.Curtain

MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J27 Continuous-time Markov processes on discrete state spaces
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