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

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.

References in corpus (2)

• Overshoots and undershoots of Lévy processes
• The law of the supremum of a stable Lévy process with no negative jumps

Cited by in corpus (1)

• First passage time law for some Lévy processes with compound Poisson: Existence of a conditional density with incomplete observation