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

Fiona Sloothaak, Vitali Wachtel, Bert Zwart

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Samenvatting

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.

Originele taal-2Engels
Pagina's (van-tot)627-651
Aantal pagina's25
TijdschriftJournal of Applied Probability
Volume55
Nummer van het tijdschrift2
DOI's
StatusGepubliceerd - 1 jun 2018

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