A coupling approach to Doob’s theorem

  • Alexei Kulik

    National Academy of Science of Ukraine, Kyiv, Ukraine
  • Michael Scheutzow

    Technische Universität Berlin, Germany


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