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Theory of Probability and Mathematical Statistics

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An estimate of the expectation of the excess of a renewal sequence generated by a time-inhomogeneous Markov chain if a square-integrable majorizing sequence exists


Author: V. V. Golomozyĭ
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 94 (2016).
Journal: Theor. Probability and Math. Statist. 94 (2017), 53-62
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/tpms/1008
Published electronically: August 25, 2017
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Abstract: We consider sufficient conditions providing the existence of the expectation of the excess of a renewal sequence for a time-inhomogeneous Markov chain with an arbitrary space of states. For such a chain, we study the behavior of the corresponding renewal process, the sequence of moments when the chain returns to a certain set $ C$. The main aim of the paper is to derive a numerical bound for the expectation of the excess of the renewal sequence defined as the time between a moment $ t$ and the first renewal after $ t$.


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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

DOI: https://doi.org/10.1090/tpms/1008
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions
Received by editor(s): April 10, 2016
Published electronically: August 25, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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