Supremum distribution of Bessel process of drifting Brownian motion

Abstrakt

Let us assume that B_t¹, B_t², B_t³ + μt is a threedimensional Brownian motion with drift μ, starting at the origin. Then X_t = ∥B_t¹ , B_t², B_t³ + μt∥, its distance from the starting point, is a diffusion with many applications. We investigate the supremum of X_t, give an infinite- series formula for its distribution function and an exact estimate of the density of this distribution in terms of elementary functions.