First-passage time asymptotics over moving boundaries for random walk bridges
Probability
2017-08-09 v1
Abstract
We study the asymptotic tail probability 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. In the latter case, a phase transition appears in the asymptotics, of which the precise nature depends on the order of distance between zero and the moving boundary.
Cite
@article{arxiv.1708.02408,
title = {First-passage time asymptotics over moving boundaries for random walk bridges},
author = {Fiona Sloothaak and Vitali Wachtel and Bert Zwart},
journal= {arXiv preprint arXiv:1708.02408},
year = {2017}
}