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

## TL;DR

This paper analyzes the asymptotic behavior of first passage times and exit probabilities for additive functionals of skew Bessel processes, extending previous results on Brownian motion to a broader class of processes.

## Contribution

It provides new asymptotic formulas for passage times and exit probabilities for additive functionals of skew Bessel processes, generalizing prior Brownian motion results.

## Key findings

- Asymptotic formulas for first passage times to fixed levels.
- Probabilities of reaching certain levels before others.
- Behavior of the process when exiting bounded intervals.

## 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.