Persistence and Exit Times for Some Additive Functionals of Skew Bessel Processes

Christophe Profeta ()
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Christophe Profeta: Université d’Evry-Val-d’Essonne, UMR CNRS 8071

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 363-390

Abstract: Abstract Let X be some homogeneous additive functional of a skew Bessel process Y. In this note, we compute the asymptotics of the first passage time of X to some fixed level b, and study the position of Y when X exits a bounded interval [a, b]. As a by-product, we obtain the probability that X reaches the level b before the level a. Our results extend some previous works on additive functionals of Brownian motion by Isozaki and Kotani for the persistence problem and by Lachal for the exit time problem.

Keywords: Bessel processes; Skew processes; Persistence problem; Exit time problem; 60J60; 60G40; 60G18 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00966-1

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