Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Oleg Butkovsky; Fabrice Wunderlich

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arXiv · 1912.06121

Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Oleg Butkovsky·Fabrice Wunderlich

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Abstract

In this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger form of ASF together with local weak irreducibility implies uniqueness of an invariant measure. The latter result is optimal in a certain sense and complements some of the corresponding results of Hairer, Mattingly (2008).

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Oleg Butkovsky, Fabrice Wunderlich. 2019-12-12. Asymptotic strong Feller property and local weak irreducibility via generalized couplings. https://arxiv.org/abs/1912.06121

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