## The Annals of Probability

### On Stopping Times for $n$ Dimensional Brownian Motion

Burgess Davis

#### Abstract

Let $\bar{X}(t) = (X_1(t),\cdots, X_n(t))$ be standard $n$ dimensional Brownian motion. Results of the following nature are proved. If $\tau$ is a stopping time for $\bar{X}(t)$ then $|\bar{X}(\tau)|$ and $(n\tau)^{\frac{1}{2}}$ are relatively close in $L^p$ if $n$ is large. Also, if $n$ is large most of the moments $EX_i(\tau)^k, i = 1,2,\cdots, n$, are about what they would be if $\bar{X}(t)$ were independent of $\tau$.

#### Article information

Source
Ann. Probab., Volume 6, Number 4 (1978), 651-659.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995485

Digital Object Identifier
doi:10.1214/aop/1176995485

Mathematical Reviews number (MathSciNet)
MR494534

Zentralblatt MATH identifier
0383.60076

JSTOR
Davis, Burgess. On Stopping Times for $n$ Dimensional Brownian Motion. Ann. Probab. 6 (1978), no. 4, 651--659. doi:10.1214/aop/1176995485. https://projecteuclid.org/euclid.aop/1176995485