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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.
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
Full Text: DOI
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