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Teoriya Veroyatnostei i ee Primeneniya, 2000, Volume 45, Issue 2, Pages 268–288
DOI: https://doi.org/10.4213/tvp463
(Mi tvp463)
 

This article is cited in 5 scientific papers (total in 5 papers)

Ratio limit theorems for self-adjoint operators and symmetric Markov chains

M. G. Shur

Moscow State Institute of Electronics and Mathematics
Abstract: A simplest ratio limit theorem is obtained for self-adjoint operators in the spaces of L2 type which leave invariant a cone of nonnegative elements. By means of the theorem we establish ratio limit theorems for symmetric Markov chains and symmetric kernels in measurable spaces. In particular, it is shown that for symmetric Harris recurrent Markov chains a result is valid which is an analogue of the known Orey theorem (1961) about discrete recurrent symmetric chains. Similar statements are valid for nonnegative symmetric quasi-Feller kernels on locally compact spaces which are Liouville in a certain sense.
Keywords: ratio limit theorem, self-adjoint operator, Harris recurrent Markov chain, symmetric kernel, quasi-Feller kernel, Liouville kernel.
Received: 14.07.1997
English version:
Theory of Probability and its Applications, 2001, Volume 45, Issue 2, Pages 273–288
DOI: https://doi.org/10.1137/S0040585X97978221
Bibliographic databases:
Language: Russian
Citation: M. G. Shur, “Ratio limit theorems for self-adjoint operators and symmetric Markov chains”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 268–288; Theory Probab. Appl., 45:2 (2001), 273–288
Citation in format AMSBIB
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\by M.~G.~Shur
\paper Ratio limit theorems for self-adjoint operators and symmetric Markov chains
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\pages 268--288
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\zmath{https://zbmath.org/?q=an:0982.60061}
\transl
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 273--288
\crossref{https://doi.org/10.1137/S0040585X97978221}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000169004700007}
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  • https://www.mathnet.ru/eng/tvp463
  • https://doi.org/10.4213/tvp463
  • https://www.mathnet.ru/eng/tvp/v45/i2/p268
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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