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Mat. Zametki, 2008, Volume 84, Issue 1, Pages 117–126 (Mi mz4076)  

Majorizing Potentials in Strong Ratio Limit Theorems

M. G. Shur

Moscow State Institute of Electronics and Mathematics

Abstract: In [1], the strong ratio limit theorems associated with Markov chains were first proved for some “test” functions with specific properties and were then generalized to a wider family of functions. In the present paper, this family is significantly extended by functions that can be majorized in a sense by the potentials of the original functions. The verification of whether a function belongs of the new family can be simplified by using small functions and their analogs. Here the traditional recurrency- or irreducibility-type requirements for the corresponding Markov chains are replaced by more flexible requirements.

Keywords: ergodic theorem, probability measure, strong ratio limit theorem, homogenous Markov chain, bounded measurable function, potential theory, Feller chain

DOI: https://doi.org/10.4213/mzm4076

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English version:
Mathematical Notes, 2008, 84:1, 116–124

Bibliographic databases:

UDC: 519.217.2
Received: 31.05.2006

Citation: M. G. Shur, “Majorizing Potentials in Strong Ratio Limit Theorems”, Mat. Zametki, 84:1 (2008), 117–126; Math. Notes, 84:1 (2008), 116–124

Citation in format AMSBIB
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