Kulik, AlexeiScheutzow, Michael2019-01-302019-01-3020151120-6330https://depositonce.tu-berlin.de/handle/11303/9048http://dx.doi.org/10.14279/depositonce-8149Dieser 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.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.en510 MathematikMarkov processinvariant measurecouplingconvergence of transition probabilitiestotal variation distanceArticle1720-0768