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2020 Couplings, generalized couplings and uniqueness of invariant measures
Michael Scheutzow
Electron. Commun. Probab. 25: 1-7 (2020). DOI: 10.1214/20-ECP363

Abstract

We provide sufficient conditions for uniqueness of an invariant probability measure of a Markov kernel in terms of (generalized) couplings. Our main theorem generalizes previous results which require the state space to be Polish. We provide an example showing that uniqueness can fail if the state space is separable and metric (but not Polish) even though a coupling defined via a continuous and positive definite function exists.

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Michael Scheutzow. "Couplings, generalized couplings and uniqueness of invariant measures." Electron. Commun. Probab. 25 1 - 7, 2020. https://doi.org/10.1214/20-ECP363

Information

Received: 26 August 2020; Accepted: 13 November 2020; Published: 2020
First available in Project Euclid: 10 December 2020

MathSciNet: MR4187722
Digital Object Identifier: 10.1214/20-ECP363

Subjects:
Primary: 60J05
Secondary: 60G10

JOURNAL ARTICLE
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