Supremum distribution of Bessel process of drifting Brownian motion
Słowa kluczowe:Drifting Brownian motion, Bessel process, supremum distribution, estimates of theta function
Let us assume that Bt1, Bt2, Bt3 + μt is a threedimensional Brownian motion with drift μ, starting at the origin. Then Xt = ∥Bt1 , Bt2, Bt3 + μt∥, its distance from the starting point, is a diffusion with many applications. We investigate the supremum of Xt, give an infinite- series formula for its distribution function and an exact estimate of the density of this distribution in terms of elementary functions.