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.
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Enriquez, N., Sabot, C. & Zindy, O. A probabilistic representation of constants in Kesten’s renewal theorem. Probab. Theory Relat. Fields 144, 581–613 (2009). https://doi.org/10.1007/s00440-008-0155-9
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DOI: https://doi.org/10.1007/s00440-008-0155-9