First passage times for subordinate Brownian motions

Details First passage times for subordinate Brownian motions First passage times for subordinate Brownian motions

2011-10-03

arxiv.org/abs/1110.0401v2

Mathematics

Probability

24 pages, 1 figure

Scientific paper

Let X_t be a subordinate Brownian motion, and suppose that the Levy measure of the underlying subordinator has completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(\tau_x > t) of first passage times \tau_x through a barrier at x > 0, and its derivatives in t. As a corollary, we examine the asymptotic behaviour of P(\tau_x > t) and its t-derivatives, either as t goes to infinity or x goes to 0.

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