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Theory of Probability and Mathematical Statistics

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On the integrability of the coupling moment for time-inhomogeneous Markov chains


Authors: V. V. Golomoziy and N. V. Kartashov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 1-12
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/S0094-9000-2015-00930-3
Published electronically: January 26, 2015
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Abstract: In this paper, we find the conditions under which the expectation of the first coupling moment for two independent, discrete, time-inhomogeneous Markov chains is finite. We consider discrete chains with the phase space $ \{0,1,\dots \}$. As the coupling moment, we understand the first moment when both chains visit the zero state at the same time.


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Additional Information

V. V. Golomoziy
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 64/13, 01601 Kyiv, Ukraine
Email: mailtower@gmail.com

N. V. Kartashov
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 64/13, 01601 Kyiv, Ukraine
Email: mykartashov@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2015-00930-3
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions
Received by editor(s): November 1, 2011
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society