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Journal of Theoretical Probability

, Volume 13, Issue 1, pp 279–309 | Cite as

Asymptotics of First-Passage Time Over a One-Sided Stochastic Boundary

  • Zoran Vondraček
Article

Abstract

We study the asymptotic behavior of the first-passage times for Brownian motion, Lévy processes and continuous martingales over one-sided increasing stochastic, as well as deterministic, boundaries. In particular, we study the first-passage time of a Brownian motion over the increasing function of its local time, give necessary and sufficient conditions for t−1/2 asymptotics, and obtain exact asymptotics for linear functions.

first-passage time stochastic boundary Brownian motion Lévy process local time continuous martingale 

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© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Zoran Vondraček

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