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# 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 + GdW
_{H}(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.} }