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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - M. G. Shur
TI  - Majorizing Potentials in Strong Ratio Limit Theorems
JO  - Matematičeskie zametki
PY  - 2008
SP  - 117
EP  - 126
VL  - 84
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a8/
LA  - ru
ID  - MZM_2008_84_1_a8
ER  - 
%0 Journal Article
%A M. G. Shur
%T Majorizing Potentials in Strong Ratio Limit Theorems
%J Matematičeskie zametki
%D 2008
%P 117-126
%V 84
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a8/
%G ru
%F MZM_2008_84_1_a8
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/

[1] M. G. Shur, “Ob uslovii Lina v silnykh predelnykh teoremakh dlya otnoshenii”, Matem. zametki, 75:6 (2004), 927–940 | MR | Zbl

[2] K.-L. Chzhun, Odnorodnye tsepi Markova, Mir, M., 1964 | MR | Zbl

[3] D. Revyuz, Tsepi Markova, RFFI, M., 1997 | MR | Zbl

[4] Zh. Neve, Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | MR | Zbl

[5] S. Orey, Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities, Van Nostrand Reinhold Math. Stud., 34, Van Nostrand Reinhold Co., London, 1971 | MR | Zbl

[6] F. Spitser, Printsipy sluchainogo bluzhdaniya, Mir, M., 1969 | MR | Zbl

[7] E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators, Cambridge Tracts in Math., 83, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[8] M. Lin, “Strong ratio limit theorems for mixing Markov operators”, Ann. Inst. H. Poincaré Sect. B (N.S.), 12:12 (1976), 181–191 | MR | Zbl

[9] W. Woess, “Random walks on infinite graphs and groups – a survey on selected topics”, Bull. London Math. Soc., 26:1 (1994), 1–60 | DOI | MR | Zbl

[10] M. G. Shur, “Predelnye teoremy dlya otnoshenii, assotsiirovannykh s samosopryazhennymi operatorami i simmetrichnymi tsepyami Markova”, Teoriya veroyatn. i ee primen., 45:2 (2000), 268–288 | MR | Zbl

[11] M. G. Shur, “Uslovie ravnomernoi integriruemosti v silnykh predelnykh teoremakh dlya otnoshenii”, Teoriya veroyatn. i ee primen., 50:3 (2005), 517–532 | MR | Zbl

[12] M. G. Shur, “Kvazifellerovskie rasshireniya markovskikh tsepei i suschestvovanie dvoistvennykh tsepei”, Matem. zametki, 69:1 (2001), 133–143 | MR | Zbl