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

Kunze, Markus

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

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Date

2011

Publication type

Journal article

Publication status

Published

Published in

Stochastics : An International Journal of Probability and Stochastic Processes ; 85 (2011), 6. - pp. 960-986. - ISSN 1744-2508. - eISSN 1744-2516

Abstract

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.

Subject (DDC)

510 Mathematics

Keywords

semilinear stochastic equation; uniqueness in law; transition semigroup; strong Feller property; invariant measure

Cite This

ISO 690

KUNZE, 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. 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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