engleski

Asymptotics of first-passage time over a one-sided stochastic boundary

We study the asymptotic behavior of the first-passage times for Brownian motion, L'evy 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.

sfirst-passage time ; stochastic boundary ; Brownian motion ; Levy processlocal time ; continuous martingale

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