SUPREMUM DISTRIBUTION OF BESSEL PROCESS OF DRIFTING
BROWNIAN MOTION
Andrzej Pyć
Grzegorz Serafin
Tomasz Żak
Abstract: Let us assume that
is a three-dimensional Brownian motion
with drift
, starting at the origin. Then
, its distance
from the starting point, is a diffusion with many applications. We investigate the
supremum of
, give an infinite-series formula for its distribution function and an
exact estimate of the density of this distribution in terms of elementary functions.
2000 AMS Mathematics Subject Classification: Primary: 60J60; Secondary:
60G70.
Keywords and phrases: Drifting Brownian motion, Bessel process, supremum
distribution, estimates of theta function.