, Volume 144, Issue 3-4, pp 581-613

A probabilistic representation of constants in Kesten’s renewal theorem

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Abstract

The aims of this paper are twofold. Firstly, we derive a probabilistic representation for the constant which appears in the one-dimensional case of Kesten’s renewal theorem. Secondly, we estimate the tail of a related random variable which plays an essential role in the description of the stable limit law of one-dimensional transient sub-ballistic random walks in random environment.