Asymptotic Stability for Non-equicontinuous Markov Semigroups

Abstract

We prove that the asymptotic stability, also known as the weak mixing, is equivalent to a lower bound condition together with the eventual continuity. The latter is a form of weak regularity for Markov–Feller semigroups that generalizes the e-property. Additionally, we provide an example of an asymptotically stable Markov semigroup with essential randomness that does not satisfy the e-property.

Keywords

Markov–Feller semigroup / Asymptotic stability / E-property / Eventual continuity

References

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Funding

National Natural Science Foundation of China(No. 11731009, 12231002)

National Key R & D Program of China(No. 2020YFA0712700)

Key Laboratory of Random Complex Structures and Data Sciences, Mathematics and Systems Science, Chinese Academy of Sciences(No. 2008DP173182)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature