Supremum distribution of Bessel process of drifting Brownian motion

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

Abstract

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.

Download article

This article

Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 201 to 222

Other articles by author

Google Scholar

zamknij

Your cart (products: 0)

No products in cart

Your cart Checkout