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An inequality for the coupling moment in the case of two inhomogeneous Markov chains


Author: V. V. Golomozyĭ
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 43-56
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/tpms/948
Published electronically: August 6, 2015
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Abstract: We consider discrete Markov chains with phase space $ \{0,1,\dots \}$ and study conditions under which the expectation of the first coupling moment for two independent discrete time inhomogeneous Markov chains is finite. The coupling moment is defined as the first time when both chains simultaneously visit the zero state. Some special cases are considered where a bound for the expectation of the coupling moment is available.


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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, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email: mailtower@gmail.com

DOI: https://doi.org/10.1090/tpms/948
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions
Received by editor(s): September 1, 2013
Published electronically: August 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society