The Annals of Probability

On a Problem of H. P. McKean: Independence of Brownian Hitting Times and Places

Loren D. Pitt

Full-text: Open access

Abstract

We show that for bounded domains $A \subseteq \mathbb{R}^N$ with $0\in A,$ if the exit time $\tau_A$ and exit place $X(\tau_A)$ are independent for a Brownian motion starting at 0, then $A$ is essentially a ball centered at 0. Extensions are given when $X(t)$ is a Brownian motion with constant drift and when $A$ is unbounded.

Article information

Source
Ann. Probab. Volume 17, Number 4 (1989), 1651-1657.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176991179

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176991179

Mathematical Reviews number (MathSciNet)
MR1048951

Zentralblatt MATH identifier
0683.60056

Subjects
Primary: 60J65: Brownian motion [See also 58J65]

Keywords
Brownian hitting times and hitting places

Citation

Pitt, Loren D. On a Problem of H. P. McKean: Independence of Brownian Hitting Times and Places. The Annals of Probability 17 (1989), no. 4, 1651--1657. doi:10.1214/aop/1176991179. http://projecteuclid.org/euclid.aop/1176991179.


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