Abstract
A semigroup approach is used to prove existence, uniqueness and boundedness of the solution of semilinear stochastic evolution equations with monotone nonlinearities. The existence and uniqueness theorem is based on Picard iteration together with results from the theory of deterministic semilinear evolution equations. The usual Gronwall inequality arguments are earned out with the aid of a Burkholder type inequality and an Ito type “energy” inequality. These two theorems are the main tools for study of semilinear stochastic evolution equations with monotone nonlinearities. In addition diverse examples which have arisen in applications are shown to satisfy the hypotheses of the theorem and consequently the results can be applied to these examples.
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