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Teoriya Veroyatnostei i ee Primeneniya, 2012, Volume 57, Issue 4, Pages 682–700
DOI: https://doi.org/10.4213/tvp4474 (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)
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DOI: https://doi.org/10.4213/tvp4474
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.
Received: 22.03.2011
English version:
Theory of Probability and its Applications, 2013, Volume 57, Issue 4, Pages 649–662
DOI: https://doi.org/10.1137/S0040585X97986205
Bibliographic databases:
Document Type: Article
MSC: 60F15, 60J05
Language: Russian
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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