Fan, Xi-Liang Non autonomous semilinear stochastic evolution equations. (English) Zbl 1320.60124 Commun. Stat., Theory Methods 44, No. 9, 1806-1818 (2015). 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 Keywords:stochastic evolution equations; mild solution; Picard approximation; factorization method PDF BibTeX XML Cite \textit{X.-L. Fan}, Commun. Stat., Theory Methods 44, No. 9, 1806--1818 (2015; Zbl 1320.60124) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.