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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 3, Pages 563–573 (Mi tvp2669)  

Short Communications

An estimate of the convergence rate in a renewal theorem for random variables defined on a Markov chain

A. E. Zaslavskii

Novosibirsk State University

Abstract: A sequence of sums of random variables with arbitrary sign defined on transitions of a homogeneous aperiodic discrete Markov chain is represented by Doeblin's method ([2],[3]) as a sequence of sums of independent random variables. The results of [5] being applied, the convergence rate in a renewal theorem ([1]) is estimated.

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English version:
Theory of Probability and its Applications, 1973, 17:3, 535–543

Bibliographic databases:

Received: 03.08.1970

Citation: A. E. Zaslavskii, “An estimate of the convergence rate in a renewal theorem for random variables defined on a Markov chain”, Teor. Veroyatnost. i Primenen., 17:3 (1972), 563–573; Theory Probab. Appl., 17:3 (1973), 535–543

Citation in format AMSBIB
\Bibitem{Zas72}
\by A.~E.~Zaslavskii
\paper An estimate of the convergence rate in a~renewal theorem for random variables defined on a~Markov chain
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 3
\pages 563--573
\mathnet{http://mi.mathnet.ru/tvp2669}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=307374}
\zmath{https://zbmath.org/?q=an:0276.60084}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 3
\pages 535--543
\crossref{https://doi.org/10.1137/1117064}


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