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arXiv · 2404.19399

Lévy processes resurrected in the positive half-line

María Emilia Caballero·Loïc Chaumont·Víctor Rivero
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Abstract

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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María Emilia Caballero, Loïc Chaumont, Víctor Rivero. 2024-09-25. Lévy processes resurrected in the positive half-line. https://arxiv.org/abs/2404.19399

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