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Mat. Zametki, 2004, Volume 75, Issue 6, Pages 927–940 (Mi mz77)  

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

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.

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

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English version:
Mathematical Notes, 2004, 75:6, 864–876

Bibliographic databases:

UDC: 519.217.2
Received: 30.04.2003

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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\pages 864--876
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    Erratum

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