Further studies on square-root boundaries for Bessel processes

TL;DR

This paper investigates the distributions of hitting times of Bessel processes with square-root boundaries, providing new proofs, factorizations, and characterizations of these distributions through decomposition techniques.

Contribution

It introduces novel decompositions and characterizations of hitting time distributions for Bessel processes with square-root boundaries, extending previous Mellin transform results.

Findings

New proofs of Mellin transform results for Bessel hitting times

Random factorizations of hitting time distributions

Characterizations of distributions related to Bessel processes

Abstract

We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distributions are linked giving a new proof of some Mellin transforms results obtained by David M. DeLong and M. Yor. Several random factorizations and characterizations of the studied distributions are established.