Stability of transition semigroups and applications to parabolic equations

Gerlach, Moritz; Glück, Jochen; Kunze, Markus

doi:10.1090/tran/8620

Stability of transition semigroups and applications to parabolic equations
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by Moritz Gerlach, Jochen Glück and Markus Kunze;

Trans. Amer. Math. Soc. 376 (2023), 153-180

DOI: https://doi.org/10.1090/tran/8620

Published electronically: October 7, 2022

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Abstract:

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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Stability of transition semigroups and applications to parabolic equations
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Abstract: