Persistence and exit times for some additive functionals of skew Bessel processes

2019/05/24 by Christophe Profeta, Profeta, Christophe
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1905.10196

arxiv created 2019/05/24 · openalex publication_date 2019/05/24 · arxiv updated 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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