Journal of Theoretical Probability

, Volume 31, Issue 3, pp 1235–1272 | Cite as

On a Multivariate Strong Renewal Theorem

  • Zhiyi ChiEmail author


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.


Renewal Regular variation Infinitely divisible Large deviations 

Mathematics Subject Classification (2010)

60K05 60F10 



The author would like to thank two referees and the AE for their careful reading of the paper and useful suggestions.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ConnecticutStorrsUSA

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