First-passage time asymptotics over moving boundaries for random walk bridges. (26th July 2018)

• Record Type: Journal Article
• Authors: Sloothaak, Fiona; Wachtel, Vitali; Zwart, Bert
• Is Part Of: Journal of applied probability. Volume 55:Number 2(2018)
• Page Start: 627
• Page End: 651
• Publication Date: 2018-07-26
• Subjects: Random walk, -- first-passage time, -- moving boundary, -- bridge; Primary 60G50, -- Secondary 60F05; 519.2
• DOI: 10.1017/jpr.2018.39
• Languages: English
• ISSNs: 0021-9002

Abstract

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 -½, 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.