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Completely asymmetric Lévy processes confined in a finite interval

Annales de l'Institut Henri Poincare (B) Probability and Statistics, 2000
Let \([0,a]\) be a finite interval and consider a Lévy process \(X_t\) which has only negative jumps (i.e., it is completely asymmetric) and admits transition densities. Write \(\psi\) for the characteristic (Laplace) exponent of \(X_t\) and denote by \(T\) the first exit time from \([0,a]\). The two-sided exit problem for such a process was studied by
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