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Teor. Veroyatnost. i Primenen., 2012, Volume 57, Issue 4, Pages 682–700 (Mi tvp4474)  

This article is cited in 1 scientific paper (total in 1 paper)

Uniform integrability for strong ratio limit theorems. III

M. G. Shur

Moscow State Institute of Electronics and Mathematics (Technical University)

Abstract: Unlike Parts I and II of this paper [Theory Probab. Appl. 50, No. 3, 436–447 (2006); translation from Teor. Veroyatn. Primen. 50, No. 3, 517–532 (2005; Zbl 1120.60028) and Theory Probab. Appl. 55, No. 3, 473–484 (2011); erratum ibid. 56, No. 1, 178 (2012); translation from Teor. Veroyatn. Primen. 55, No. 3, 446–461 (2010; Zbl 1247.60040)], which dealt with strong limit theorems for ratios (SLTR) in the traditional sense, now we propose new SLTR with particular parametric sets. The peculiarity of these theorems is that their statements ignore some values of time parameter that form a particular set of density 0. SLTR of this type for random walks on unimodular locally compact groups are given as an illustration of the general theory.

Keywords: Markov chain; strong limit theorem for ratios; random walk on a group.

DOI: https://doi.org/10.4213/tvp4474

Full text: PDF file (226 kB)
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English version:
Theory of Probability and its Applications, 2013, 57:4, 649–662

Bibliographic databases:

MSC: 60F15, 60J05
Received: 22.03.2011

Citation: M. G. Shur, “Uniform integrability for strong ratio limit theorems. III”, Teor. Veroyatnost. i Primenen., 57:4 (2012), 682–700; Theory Probab. Appl., 57:4 (2013), 649–662

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. M. G. Shur, “Exponentials and $R$-recurrent random walks on groups”, Theory Probab. Appl., 61:3 (2017), 505–513  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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