First passage times for subordinate Brownian motions
Probability
2017-02-15 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1110.0401,
title = {First passage times for subordinate Brownian motions},
author = {Mateusz Kwasnicki and Jacek Malecki and Michal Ryznar},
journal= {arXiv preprint arXiv:1110.0401},
year = {2017}
}
Comments
24 pages, 1 figure