Supremum distribution of Bessel process of drifting Brownian motion
Abstract
Let (B(1)t ;B(2)t ;B(3)t + μ t) be a three-dimensional Brownian motion with drift μ, starting at the origin. Then Xt = ||(B(1)t ;B(2)t ;B(3)t +μ t)||, its distance from the starting point, is a diffusion with many applications. We investigate the distribution of the supremum of (Xt), give an infinite-series formula for its density and an exact estimate by elementary functions.
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