On the range of Brownian motion and its inverse process (Q1067317)

This paper investigates various relationships between Brownian motion, its range process \((M_ t-m_ t)\) and the three dimensional Bessel process. The respective first passage time processes are compared via their Poisson measures. For \(\theta\) the first hitting time of some level by the range process, the Brownian path prior to \(\theta\) is considered, and a path decomposition result is obtained.