This article is cited 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.

MSC: 60F15, 60J05

Received: 22.03.2011

DOI: 10.4213/tvp4474

 English version: Theory of Probability and its Applications, 2013, 57:4, 649–662

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