First passage time law for some jump-diffusion processes : existence of a density
Probability
2012-01-13 v3
Abstract
Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a density (defective when E(X1) < 0) with respect to the Lebesgue measure.
Keywords
Cite
@article{arxiv.0904.1669,
title = {First passage time law for some jump-diffusion processes : existence of a density},
author = {Laure Coutin and Diana Dorobantu},
journal= {arXiv preprint arXiv:0904.1669},
year = {2012}
}