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🆕 Date Issued:
2015
🗄 In DepositOnce:2019-01-30
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A coupling approach to Doob’s theorem

Kulik, Alexei; Scheutzow, Michael

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.
Markov processinvariant measurecouplingconvergence of transition probabilitiestotal variation distance
Published in: Rendiconti lincei - Matematica e applicazioni, 10.4171/RLM/694, European Mathematical Society
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