Lévy processes resurrected in the positive half-line

María Emilia Caballero, Loïc Chaumont, Víctor Rivero

Published 2024-04-30Version 1

A L\'evy 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 L\'evy process. Then in many important classes of L\'evy processes, we give conditions for absorption and conditions for non absorption bearing on the characteristics of the initial L\'evy process.