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April, 1975 A Stopped Brownian Motion Formula
Howard M. Taylor
Ann. Probab. 3(2): 234-246 (April, 1975). DOI: 10.1214/aop/1176996395

Abstract

We determine $E\lbrack \exp (\alpha X(T) - \beta T) \rbrack$ where $X(t)$ is a Brownian motion having arbitrary drift and variance and $T$ is the first time the process drops a specified amount below its maximum to date. From this result, the moments of $X(T)$ and $T$ and some asymptotic distributions may be found. Applications in process control and financial management are mentioned.

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Howard M. Taylor. "A Stopped Brownian Motion Formula." Ann. Probab. 3 (2) 234 - 246, April, 1975. https://doi.org/10.1214/aop/1176996395

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60072
MathSciNet: MR375486
Digital Object Identifier: 10.1214/aop/1176996395

Keywords: 60 , Brownian motion , J65 , moment generating function , stopping time

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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