On the limit law of a random walk conditioned to reach a high level

Serguei Foss, Anatolii A. Puhalskii

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a random walk with a negative drift and with a jump distribution which under Cramr's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lvy process conditioned not to overshoot level 1. © 2010 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)288-313
Number of pages26
JournalStochastic Processes and their Applications
Volume121
Issue number2
DOIs
Publication statusPublished - Feb 2011

Keywords

  • borderline case
  • convergence of conditional laws
  • Random walk with negative drift
  • spectrally positive lvy process conditioned not to overshoot
  • tail asymptotics for the supremum

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