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August, 1977 Formulas for Stopped Diffusion Processes with Stopping Times Based on the Maximum
John P. Lehoczky
Ann. Probab. 5(4): 601-607 (August, 1977). DOI: 10.1214/aop/1176995770

Abstract

The joint Laplace transform of $T$ and $X(T)$ is derived where $X(\bullet)$ is a time homogeneous diffusion process and $T$ is the first time the process falls a specified amount below its current maximum. This generalizes the work of Taylor. The distribution of the maximum at $T$ is shown to be exponential for Brownian motion. Formulas for more general stopping times based on the current maximum are given.

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John P. Lehoczky. "Formulas for Stopped Diffusion Processes with Stopping Times Based on the Maximum." Ann. Probab. 5 (4) 601 - 607, August, 1977. https://doi.org/10.1214/aop/1176995770

Information

Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0367.60093
MathSciNet: MR458570
Digital Object Identifier: 10.1214/aop/1176995770

Subjects:
Primary: 60J60
Secondary: 60G40 , 60H10

Keywords: diffusion process , Laplace transform , Stochastic differential equation , stopping time

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 4 • August, 1977
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