A coupling approach to Doob's theorem

作者：Kulik Alexei^*; Scheutzow Michael

来源：Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2015, 26(1): 83-92.

DOI：10.4171/RLM/694

• Markov process
• invariant measure
• coupling
• convergence of transition probabilities
• total variation distance

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 mu converge to mu 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 mu-almost all initial conditions.

• 出版日期2015