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Existence and uniqueness of the solution for stochastic equations on Banach spaces. (English) Zbl 0886.60064
Summary: The present paper is concerned with the existence and uniqueness of the solution for the stochastic equation $$dX= (AX+ F(X,t))dt +G(X,t)dW$$, where $$A$$ is the generator of a $$C_0$$-semigroup on a Hilbert space $$H$$, $$F$$ and $$G$$ are defined on some subspace of $$H$$, and $$W$$ stands for a cylindrical Wiener process on $$H$$. As a special case we consider a stochastic reaction diffusion equation.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35K05 Heat equation
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