First-passage time asymptotics over moving boundaries for random walk bridges

Fiona Sloothaak, Vitali Wachtel, Bert Zwart

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study the asymptotic tail behavior of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent-1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary.

Original languageEnglish
Pages (from-to)627-651
Number of pages25
JournalJournal of Applied Probability
Volume55
Issue number2
DOIs
Publication statusPublished - 1 Jun 2018

Keywords

  • bridge
  • first-passage time
  • moving boundary
  • Random walk

Fingerprint Dive into the research topics of 'First-passage time asymptotics over moving boundaries for random walk bridges'. Together they form a unique fingerprint.

  • Cite this