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

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

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