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 Tx the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of Tx has a density (defective when E(X1) < 0) with respect to the Lebesgue measure.
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