Asymptotics of the densities of the first passage time distributions for Bessel diffusions

TL;DR

This paper derives the asymptotic behavior of the densities of first passage times for Bessel processes, providing uniform results for various starting positions as time approaches infinity.

Contribution

It introduces new asymptotic formulas for the densities of first passage times of Bessel diffusions, valid uniformly across initial positions.

Findings

Asymptotic forms of passage time densities as time tends to infinity

Uniform validity of results for different starting points

Enhanced understanding of Bessel process hitting times

Abstract

This paper concerns the first passage times of Bessel processes to a point on the positive real line. We are interested in the case when the process starts at a position on its right and compute the densities of the distributions of the passage time to obtain the asymptotic forms of them as time tends to infinity that are valid uniformly for the starting position.