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

By F. Sloothaak, Vitali Wachtel and Bert Zwart

Abstract

textabstractWe 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

Topics: Bridge, First-passage time, Moving boundary, Random walk
Year: 2018
DOI identifier: 10.1017/jpr.2018.39
OAI identifier:
Provided by: NARCIS
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