Supremum distribution of Bessel process of drifting Brownian motion

  1. Andrzej Pyć
  2. Grzegorz Serafin
  3. Tomasz Żak


Let us assume that (Bt(1), Bt(2), Bt(3) + μt) is a threedimensional Brownian motion with drift μ, starting at the origin. Then Xt = ∥(Bt(1) , Bt(2), Bt(3) + 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.

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Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 201 to 222

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