On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions

S. Zachary, S. G. Foss

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some ? > 0 to a subclass of the class S ? (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the "spatially local" asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds. © 2006 Springer Science+Business Media, Inc.

Original languageEnglish
Pages (from-to)1034-1041
Number of pages8
JournalSiberian Mathematical Journal
Volume47
Issue number6
DOIs
Publication statusPublished - Nov 2006

Keywords

  • Exact asymptotics
  • Ruin probability
  • Supremum of random walk

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