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Non autonomous semilinear stochastic evolution equations. (English) Zbl 1320.60124
Summary: In this article, we first give a version with continuous paths for the stochastic convolution \(\int^{t}_{0} U(t,s)\phi (s)dW(s)\) driven by a Wiener process \(W\) in a Hilbert space under weaker conditions. Based on the Picard approximation and the factorization method, we prove the existence, uniqueness and regularity of mild solutions for non-autonomous semilinear stochastic evolution equations with more general assumptions on the coefficients. As an application, we obtain the Feller property of the associated semigroup.
MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
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