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Main Title: A coupling approach to Doob’s theorem
Author(s): Kulik, Alexei
Scheutzow, Michael
Type: Article
Language Code: en
Abstract: We provide a coupling proof of Doob’s theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure μ converge to μ in the total variation distance. In addition we show that non-singularity (rather than equivalence) of the transition probabilities suffices to ensure convergence of the transition probabilities for μ-almost all initial conditions.
Issue Date: 2015
Date Available: 30-Jan-2019
DDC Class: 510 Mathematik
Subject(s): Markov process
invariant measure
convergence of transition probabilities
total variation distance
Journal Title: Rendiconti lincei - Matematica e applicazioni
Publisher: European Mathematical Society
Publisher Place: Zürich
Volume: 26
Issue: 1
Publisher DOI: 10.4171/RLM/694
Page Start: 83
Page End: 92
EISSN: 1720-0768
ISSN: 1120-6330
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Stochastische Analysis » Publications

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