Maximal coupling and stability of discrete non-homogeneous Markov chains

Golomozyĭ, V.; Kartashov, M.

doi:10.1090/tpms/963

Maximal coupling and stability of discrete non-homogeneous Markov chains

Authors: V. V. Golomozyĭ and M. V. Kartashov
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 91 (2015), 17-27
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/tpms/963
Published electronically: February 3, 2016
MathSciNet review: 3364120
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Abstract: We consider two time non-homogeneous discrete Markov chains whose one-step transition probabilities are close in the uniform total variation norm. The problem of stability of the transition probabilities for an arbitrary number of steps is investigated. The main assumption is the uniform mixing. We prove that the uniform difference between the distributions of the chains after an arbitrary number of steps does not exceed $\varepsilon /(1-\rho )$, where $\varepsilon$ is the uniform distance between transition matrices and $\rho$ is the uniform mixing coefficient. The proofs are based on the maximal coupling procedure that maximize the one-step coupling probabilities.

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