Maximal coupling and 𝑉-stability of discrete nonhomogeneous Markov chains

Golomozyĭ, V.; Kartashov, M.

doi:10.1090/tpms/992

Maximal coupling and $V$-stability of discrete nonhomogeneous Markov chains

Authors: V. V. Golomozyĭ and M. V. Kartashov
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 93 (2016), 19-31
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/tpms/992
Published electronically: February 7, 2017
MathSciNet review: 3553437
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Abstract: Two time-nonhomogeneous discrete Markov chains whose one-step transition probabilities are close in the $V$-variation norm are considered. The problem of stability of the expectation of $f(X_n)$ with $|f|\le V$ is studied for Markov chains. The main assumption imposed on a Markov chain is the $V$-mixing. The proofs are based on the maximal coupling procedure that maximize the one-step coupling probabilities.

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