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

F. Sloothaak, B. Zwart, V. Wachtel

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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.
Originele taal-2Engels
Artikelnummer1708.02408
Aantal pagina's22
TijdschriftarXiv
Nummer van het tijdschrift1708.02408
StatusGepubliceerd - 9 aug 2017

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