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

Golomozyĭ, V.

doi:10.1090/tpms/1008

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
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
MathSciNet review: 3553453
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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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