Stability of transition semigroups and applications to parabolic equations
- 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 stochas-tic 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.
Author details: | Moritz GerlachORCiDGND, Jochen GlückORCiDGND, Markus KunzeORCiD |
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DOI: | https://doi.org/10.1090/tran/8620 |
ISSN: | 0002-9947 |
ISSN: | 1088-6850 |
Title of parent work (English): | Transactions of the American Mathematical Society |
Publisher: | American Mathematical Soc. |
Place of publishing: | Providence |
Publication type: | Article |
Language: | English |
Year of first publication: | 2023 |
Publication year: | 2023 |
Release date: | 2024/07/03 |
Tag: | Transition probabilities; asymptotic; behavior; invariant measure; parabolic equations; strong Feller property |
Volume: | 376 |
Issue: | 1 |
Number of pages: | 28 |
First page: | 153 |
Last Page: | 180 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |