Abstract
Let ($X_t, t \geq 0)$ be a Lévy process with compound Poisson process and $τ_x$ be the first passage time of a fixed level $x > 0$ by ($X_t, t \geq 0$). We prove that the law of $τ_x$ has a density (defective when $\mathbb{E}(X_{1})\ < 0)$ with respect to the Lebesgue measure.
Citation
Laure Coutin. Diana Dorobantu. "First passage time law for some Lévy processes with compound Poisson: Existence of a density." Bernoulli 17 (4) 1127 - 1135, November 2011. https://doi.org/10.3150/10-BEJ323
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