Hitting times for Bessel processes

Abstract

We study the density of the first time that a Bessel bridge of dimension δ ∈ R hits a constant boundary. We do so by first writing the stochastic differential equations to analyze the Bessel process for every δ ∈ R. Then, we make use of a change of measure using a Doob's h-transform. The technique covers processes which are solutions of a certain class of stochastic differential equations. Another example we present is for the 3-dimensional Bessel process with drift.