Geodesic
Majorizing Potentials in Strong Ratio Limit Theorems
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 117-126

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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, bounded measurable function, potential theory
Mots-clés : homogenous Markov chain, Feller chain. 
@article{MZM_2008_84_1_a8,
     author = {M. G. Shur},
     title = {Majorizing {Potentials} in {Strong} {Ratio} {Limit} {Theorems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {117--126},
     publisher = {mathdoc},
     volume = {84},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a8/}
}
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M. G. Shur. Majorizing Potentials in Strong Ratio Limit Theorems. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 117-126. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a8/