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August, 1978 On Stopping Times for $n$ Dimensional Brownian Motion
Burgess Davis
Ann. Probab. 6(4): 651-659 (August, 1978). DOI: 10.1214/aop/1176995485

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 $\tau$.

Citation

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Burgess Davis. "On Stopping Times for $n$ Dimensional Brownian Motion." Ann. Probab. 6 (4) 651 - 659, August, 1978. https://doi.org/10.1214/aop/1176995485

Information

Published: August, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0383.60076
MathSciNet: MR494534
Digital Object Identifier: 10.1214/aop/1176995485

Subjects:
Primary: 60J65
Secondary: 31B05, 60J40

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • August, 1978
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