Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
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
V. V. Golomozyĭ
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Abstract: In this paper, we consider conditions which satisfy finitness of theexpectation of the excess of the renewal sequence of the time-inhomogeneous Markov chain. We consider a chain with an arbitrary state space, and some set C. Within this chain we learn a behaviour of a renewal process - a sequence of moments in which chain is returning to C. Main goal of an article to define numerical estimate for the expectati- on for the renewal sequence excess - a time to wait from the moment t until the new renewal.
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions
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