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A simple proof of Pitman's 2M–X theorem

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  01 July 2016

J. P. Imhof
J. P. Imhof*
Affiliation:
University of Geneva
*
∗ Postal address: Section de Mathématiques, Case postale 240, 1211 Geneva 24, Switzerland.
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Abstract

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Pitman has shown that if X is Brownian motion with maximum process M, then 2M – X is a BES0(3) process. We show that this can be seen by looking at finite-dimensional densities.

Keywords

BROWNIAN MOTIONBESSEL PROCESSDENSITY FACTORIZATIONS

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60J65: Brownian motion
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 499 - 501
Copyright
Copyright © Applied Probability Trust 1992 

References

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