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

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2011
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Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik
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semilinear stochastic equation; uniqueness in law; transition semigroup; strong Feller property; invariant measure
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ISO 690KUNZE, Markus, 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. 2011, 85(6), pp. 960-986. ISSN 1744-2508. eISSN 1744-2516. Available under: doi: 10.1080/17442508.2012.712973
BibTex
@article{Kunze2011-01-12T14:29:08ZPertu-41252,
  year={2011},
  doi={10.1080/17442508.2012.712973},
  title={Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces},
  number={6},
  volume={85},
  issn={1744-2508},
  journal={Stochastics : An International Journal of Probability and Stochastic Processes},
  pages={960--986},
  author={Kunze, Markus}
}
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