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

Laure Coutin (1) , Diana Dorobantu (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: Lévy process; jump-diffusion process; hitting time law

Domaines: Probabilités [math.PR]

Laure Coutin, Diana Dorobantu. First passage time law for some jump-diffusion processes : existence of a density. Bernoulli, 2011, 17 (4), pp.1127-1135. ⟨10.3150/10-BEJ323⟩. ⟨hal-00374879v3⟩