First passage time law for some jump-diffusion processes : existence of a density

Details First passage time law for some jump-diffusion processes : existence of a density First passage time law for some jump-diffusion processes : existence of a density

2009-04-10

arxiv.org/abs/0904.1669v3

Bernoulli 17, 4 (2011) 1127-1135

Mathematics

Probability

Scientific paper

10.3150/10-BEJ323

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.

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