On a Multivariate Strong Renewal Theorem

Zhiyi Chi ()
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Zhiyi Chi: University of Connecticut

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1235-1272

Abstract: Abstract This paper takes the so-called probabilistic approach to the strong renewal theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of lattice–nonlattice composition of a distribution. A general bound is derived to control the so-called small-n contribution, which arises from random walk paths that have a relatively small number of steps but make large cumulative moves. The asymptotic negligibility of the small-n contribution is essential to the SRT. Applications of the SRT are given, including some that provide a unified treatment to known results but with substantially weaker assumptions.

Keywords: Renewal; Regular variation; Infinitely divisible; Large deviations; 60K05; 60F10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0754-4

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