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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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##### References:
 [1] Barbu D., Portugal. Math. 55 pp 411– (1998) [2] DOI: 10.1023/A:1021723421437 · Zbl 1001.60068 · doi:10.1023/A:1021723421437 [3] DOI: 10.1080/17442508708833480 · Zbl 0634.60053 · doi:10.1080/17442508708833480 [4] DOI: 10.1016/j.jfa.2009.01.007 · Zbl 1193.47047 · doi:10.1016/j.jfa.2009.01.007 [5] DOI: 10.1017/CBO9780511666223 · doi:10.1017/CBO9780511666223 [6] DOI: 10.1017/CBO9780511662829 · Zbl 0849.60052 · doi:10.1017/CBO9780511662829 [7] Frieler K., Solutions of stochastic differential equations in infinite dimensional Hilbert spaces and their dependence on initial data (2002) [8] DOI: 10.1016/0022-247X(82)90041-5 · Zbl 0497.93055 · doi:10.1016/0022-247X(82)90041-5 [9] Marinelli C., Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise (2010) · Zbl 1186.60060 [10] DOI: 10.1007/978-1-4612-5561-1 · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1 [11] Seidler J., Math. Bohemica 118 pp 67– (1993) [12] DOI: 10.1016/0022-0396(92)90148-G · Zbl 0744.34052 · doi:10.1016/0022-0396(92)90148-G [13] DOI: 10.1016/j.jmaa.2009.09.008 · Zbl 1185.60065 · doi:10.1016/j.jmaa.2009.09.008
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