The probability of exceeding a High boundary on a random time interval for a heavy-tailed random walk

Serguei Fos, Zbigniew Palmowski, Stan Zachary

Research output: Contribution to journalLiterature review

19 Citations (Scopus)

Abstract

We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. © Institute of Mathematical Statistics, 2005.

Original languageEnglish
Pages (from-to)1936-1957
Number of pages22
JournalAnnals of Applied Probability
Volume15
Issue number3
DOIs
Publication statusPublished - Aug 2005

Keywords

  • Boundary
  • Random walk
  • Ruin probability
  • Subexponential distributions

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