A coupling approach to Doob’s theorem
Alexei Kulik
National Academy of Science of Ukraine, Kyiv, UkraineMichael Scheutzow
Technische Universität Berlin, Germany
![A coupling approach to Doob’s theorem cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-26-issue-1.png&w=3840&q=90)
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 converge to 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 -almost all initial conditions.
Cite this article
Alexei Kulik, Michael Scheutzow, A coupling approach to Doob’s theorem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 1, pp. 83–92
DOI 10.4171/RLM/694