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

Fingerprint

First Passage Time
Moving Boundary
Random walk
Tail Behavior
Asymptotic Behavior
Regularly Varying Function
Slowly Varying Function
Zero
Increment
Tail
Phase Transition
Exponent
First passage time
Tail behavior

Keywords

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

Cite this

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First-passage time asymptotics over moving boundaries for random walk bridges. / Sloothaak, Fiona; Wachtel, Vitali; Zwart, Bert.

In: Journal of Applied Probability, Vol. 55, No. 2, 01.06.2018, p. 627-651.

Research output: Contribution to journalArticleAcademicpeer-review

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