## The Annals of Probability

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

Loren D. Pitt

#### 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

http://projecteuclid.org/euclid.aop/1176991179

Digital Object Identifier
doi:10.1214/aop/1176991179

Mathematical Reviews number (MathSciNet)
MR1048951

Zentralblatt MATH identifier
0683.60056

JSTOR