M. G. Shur, “On the Lin Condition in Strong Ratio Limit Theorems”, Mat. Zametki, 75:6 (2004), 927–940; Math. Notes, 75:6 (2004), 864

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Matematicheskie Zametki, 2004, Volume 75, Issue 6, Pages 927–940
DOI: https://doi.org/10.4213/mzm77 (Mi mzm77)

This article is cited in 4 scientific papers (total in 5 papers)

On the Lin Condition in Strong Ratio Limit Theorems

M. G. Shur

Moscow State Institute of Electronics and Mathematics

Full-text PDF (238 kB) Citations (5)

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DOI: https://doi.org/10.4213/mzm77

Abstract: A new version of strong limit theorems for Lin ratios (1976) free of former restrictions such as the absolute continuity of the measures in question or the conservativeness of the corresponding operators is presented. As the most original statement of the paper (Theorem 5) states, one of the two basic Lin conditions holds automatically for a wide class of Markov chains and, in particular, for many random walks on groups. The proof is based on a substantial development of the author"s results (1980) concerning the behavior of multistep transition probabilities.

Received: 30.04.2003

English version:
Mathematical Notes, 2004, Volume 75, Issue 6, Pages 864–876
DOI: https://doi.org/10.1023/B:MATN.0000030995.23171.d6

Bibliographic databases:

UDC: 519.217.2

Language: Russian

Citation: M. G. Shur, “On the Lin Condition in Strong Ratio Limit Theorems”, Mat. Zametki, 75:6 (2004), 927–940; Math. Notes, 75:6 (2004), 864–876

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm77

https://doi.org/10.4213/mzm77

https://www.mathnet.ru/eng/mzm/v75/i6/p927

Erratum

Letter to the editor
M. G. Shur
Mat. Zametki, 2010, 87:1, 156

This publication is cited in the following 5 articles:

M. G. Shur, “Two theorems on convergence parameter of an irreducible Markov chain”, Theory Probab. Appl., 58:1 (2014), 159–164
M. G. Shur, “Letter to the editor”, Math. Notes, 87:1 (2010), 151–151
M. G. Shur, “Convergence Parameter Associated with a Markov Chain and a Family of Functions”, Math. Notes, 87:2 (2010), 271–280
M. G. Shur, “Majorizing Potentials in Strong Ratio Limit Theorems”, Math. Notes, 84:1 (2008), 116–124
M. G. Shur, “Uniform integrability condition in strong ration limit theorems”, Theory Probab. Appl., 50:3 (2006), 436–447

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	206
References:	65
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