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December 2001 Marginal Densities of the Least Concave Majorant of Brownian Motion
Chris Carolan, Richard Dykstra
Ann. Statist. 29(6): 1732-1750 (December 2001). DOI: 10.1214/aos/1015345960

Abstract

A clean, closed form, joint density is derived for Brownian motion, its least concave majorant, and its derivative, all at the same fixed point. Some remarkable conditional and marginal distributions follow from this joint density. For example, it is shown that the height of the least concave majorant of Brownian motion at a fixed time point has the same distribution as the distance from the Brownian motion path to its least concave majorant at the same fixed time point. Also, it is shown that conditional on the height of the least concave majorant of Brownian motion at a fixed time point, the left-hand slope of the least concave majorant of Brownian motion at the same fixed time point is uniformly distributed.

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Chris Carolan. Richard Dykstra. "Marginal Densities of the Least Concave Majorant of Brownian Motion." Ann. Statist. 29 (6) 1732 - 1750, December 2001. https://doi.org/10.1214/aos/1015345960

Information

Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1044.60072
MathSciNet: MR1891744
Digital Object Identifier: 10.1214/aos/1015345960

Subjects:
Primary: 62E15
Secondary: 62H10

Keywords: Brownian motion , least concave majorant , likelihood ratio ordering , stochastic ordering

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2001
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