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Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces

Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces

Type of Publication: Journal article
Publication status: Published
Author: Kunze, Markus C.
Year of publication: 2011
Published in: Stochastics : An International Journal of Probability and Stochastic Processes ; 85 (2011), 6. - pp. 960-986. - ISSN 1744-2508. - eISSN 1744-2516
ArXiv-ID: arXiv:1101.2369v2
DOI (citable link): https://dx.doi.org/10.1080/17442508.2012.712973
Summary:
We prove a Miyadera-Voigt type perturbation theorem for strong Feller semigroups. Using this result, we prove well-posedness of the semilinear stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdWH(t) on a separable Banach space E, assuming that F is bounded and measurable and that the associated linear equation, i.e. the equation with F = 0, is well-posed and its transition semigroup is strongly Feller and satisfies an appropriate gradient estimate. We also study existence and uniqueness of invariant measures for the associated transition semigroup.
MSC Classification: 60H15; 60J35
Subject (DDC): 510 Mathematics
Keywords: semilinear stochastic equation; uniqueness in law; transition semigroup; strong Feller property; invariant measure

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KUNZE, Markus C., 2011. Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces. In: Stochastics : An International Journal of Probability and Stochastic Processes. 85(6), pp. 960-986. ISSN 1744-2508. eISSN 1744-2516. Available under: doi: 10.1080/17442508.2012.712973

@article{Kunze2011-01-12T14:29:08ZPertu-41252, title={Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces}, year={2011}, doi={10.1080/17442508.2012.712973}, number={6}, volume={85}, issn={1744-2508}, journal={Stochastics : An International Journal of Probability and Stochastic Processes}, pages={960--986}, author={Kunze, Markus C.} }

Kunze, Markus C. We prove a Miyadera-Voigt type perturbation theorem for strong Feller semigroups. Using this result, we prove well-posedness of the semilinear stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW<sub>H</sub>(t) on a separable Banach space E, assuming that F is bounded and measurable and that the associated linear equation, i.e. the equation with F = 0, is well-posed and its transition semigroup is strongly Feller and satisfies an appropriate gradient estimate. We also study existence and uniqueness of invariant measures for the associated transition semigroup. Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces 2018-02-06T13:22:47Z 2018-02-06T13:22:47Z eng Kunze, Markus C. 2011-01-12T14:29:08Z

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