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On the semigroup approach to stochastic evolution equations. (English) Zbl 0591.60054
Stochastic space-time models and limit theorems, Math. Appl., D. Reidel Publ. Co. 19, 95-139 (1985).

[For the entire collection see Zbl 0582.00017.]

The author considers a class of stochastic evolution equations in which the stochastic term is state independent, but need only be finitely additive on the state space H, e.g. the case of cylindrical Brownian motion on H. In addition he allows for delays in the state variables and also discusses the nonlinear case. He obtains well defined solutions by enlarging the state space to a strong dual of a nuclear Fréchet space. The set up is illustrated by several examples from the literature.

Reviewer: R.Curtain
MSC:
60H15Stochastic partial differential equations
60G44Martingales with continuous parameter