Lévy processes resurrected in the positive half-line
Processus de Lévy ressuscités dans la demi-droite positive
Résumé
A Lévy processes resurrected in the positive half-line is a Markov process obtained by removing
successively all jumps that make it negative. A natural question, given this construction, is whether
the resulting process is absorbed at 0 or not. We first describe the law of the resurrected process
in terms of that of the initial Lévy process. Then in many important classes of Lévy processes,
we give conditions for absorption and conditions for non absorption bearing on the characteristics of the
initial Lévy process.
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