
arXiv: 1603.02506
Let be $(X_t, t\geq 0)$ be a L��vy process which is the sum of a Brownian motion with drift and a compound Poisson process. We consider the first passage time $��_x$ at a fixed level $x>0$ by $(X_t, t\geq 0)$ and $K_x:= X_{��_x}-x$ the overshoot and $L_x:= x-X_{��_x^-}$ the undershoot. We first study the regularity of the density of the first passage time. Secondly, we calculate the joint law of $(��_x, K_x, L_x).$
Probability (math.PR), FOS: Mathematics, Mathematics - Probability
Probability (math.PR), FOS: Mathematics, Mathematics - Probability
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