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


Authors: V. V. Golomozyĭ and M. V. Kartashov
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
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
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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 $ \vert f\vert\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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Additional Information

V. V. Golomozyĭ
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: mailtower@gmail.com

M. V. Kartashov
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: mailtower@gmail.com

DOI: https://doi.org/10.1090/tpms/992
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions, test functions
Received by editor(s): March 20, 2015
Published electronically: February 7, 2017
Additional Notes: The paper was prepared following the talk at the International Conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
Article copyright: © Copyright 2017 American Mathematical Society