The probability distributions of the first hitting times of Bessel processes

TL;DR

This paper derives explicit formulas for the distribution functions and densities of the first hitting times of Bessel processes, extending classical results to all cases using Bessel function zeros.

Contribution

It provides comprehensive explicit expressions for the first hitting time distributions of Bessel processes, covering all cases and extending previous classical results.

Findings

Explicit distribution functions for Bessel process hitting times.

Density formulas involving zeros of Bessel functions.

Extension of classical results to all Bessel process cases.

Abstract

We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover all the cases.