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

Zoran Vondraček ()

Journal of Theoretical Probability, 2000, vol. 13, issue 1, 279-309

Abstract: 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.

Keywords: first-passage time; stochastic boundary; Brownian motion; Lévy process; local time; continuous martingale (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007747312770

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