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Stability of transition semigroups and applications to parabolic equations

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2023

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Gerlach, Moritz
Glück, Jochen

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Transactions of the American Mathematical Society (TRAN). American Mathematical Society (AMS). 2023, 376(1), pp. 153-180. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/8620

Zusammenfassung

This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochastic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.

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510 Mathematik

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ISO 690GERLACH, Moritz, Jochen GLÜCK, Markus KUNZE, 2023. Stability of transition semigroups and applications to parabolic equations. In: Transactions of the American Mathematical Society (TRAN). American Mathematical Society (AMS). 2023, 376(1), pp. 153-180. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/8620
BibTex
@article{Gerlach2023Stabi-59154,
  year={2023},
  doi={10.1090/tran/8620},
  title={Stability of transition semigroups and applications to parabolic equations},
  number={1},
  volume={376},
  issn={0002-9947},
  journal={Transactions of the American Mathematical Society (TRAN)},
  pages={153--180},
  author={Gerlach, Moritz and Glück, Jochen and Kunze, Markus}
}
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