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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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