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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 1, Pages 53–68 (Mi smj1167)  
This article is cited in 2 scientific papers (total in 2 papers)

On transience conditions for Markov chains and random walks

D. É. Denisova, S. G. Fossba

a Heriot Watt University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (264 kB) Citations (2)
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Abstract: We prove a new transience criterion for Markov chains on an arbitrary state space and give a corollary for real-valued chains. We show by example that in the case of a homogeneous random walk with infinite mean the proposed sufficient conditions are close to those necessary. We give a new proof of the well-known criterion for finiteness of the supremum of a random walk.
Keywords: Markov chain, martingale, transience, uniform integrability, test function, random walk.
Received: 15.08.2001
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 1, Pages 44–57
DOI: https://doi.org/10.1023/A:1022008203109
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: D. É. Denisov, S. G. Foss, “On transience conditions for Markov chains and random walks”, Sibirsk. Mat. Zh., 44:1 (2003), 53–68; Siberian Math. J., 44:1 (2003), 44–57
Citation in format AMSBIB
\Bibitem{DenFos03}
\by D.~\'E.~Denisov, S.~G.~Foss
\paper On transience conditions for Markov chains and random walks
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 1
\pages 53--68
\mathnet{http://mi.mathnet.ru/smj1167}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1967606}
\zmath{https://zbmath.org/?q=an:1084.60532}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 1
\pages 44--57
\crossref{https://doi.org/10.1023/A:1022008203109}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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