Occupation times of balls by Brownian motion with drift

Chuancun Yin*, Sung Nok CHIU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Let X = {Xt, t ≥ 0} be a d-dimensional (d ≥ 2) standard Brownian motion with drift c started at a fixed x, and BR = {x ∈ ℝd : \x\ < R}, the ball centered at 0 with radius R. Consider the distributions of TR(t) and TR(∞), where TR(t) denotes the time spent by X in BR up to time t and TR(∞) the total time of X spent in BR. Explicit formulas for the Laplace transform of TR(∞) and the double Laplace transform of TR(t) are obtained.

Original languageEnglish
Pages (from-to)47-56
Number of pages10
JournalChinese Annals of Mathematics. Series B
Issue number1
Publication statusPublished - 2001

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Ball
  • Brownian motion with drift
  • Laplace transform
  • Occupation time


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