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

Fiona Sloothaak, Vitali Wachtel, Bert Zwart

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1 Jun 2018


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


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