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October 1998 Random Brownian scaling identities and splicing of Bessel processes
Jim Pitman, Marc Yor
Ann. Probab. 26(4): 1683-1702 (October 1998). DOI: 10.1214/aop/1022855878

Abstract

An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion and second by replacing the reflecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The first extension is related to two different constructions of Itô’s law of Brownian excursions, due to Williams and Bismut, each involving back-to-back splicing of fragments of two independent three-dimensional Bessel processes. Generalizations of both splicing constructions are described, which involve Bessel processes and Bessel bridges of arbitrary positive real dimension.

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Jim Pitman. Marc Yor. "Random Brownian scaling identities and splicing of Bessel processes." Ann. Probab. 26 (4) 1683 - 1702, October 1998. https://doi.org/10.1214/aop/1022855878

Information

Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0937.60079
MathSciNet: MR1675059
Digital Object Identifier: 10.1214/aop/1022855878

Subjects:
Primary: 60J65
Secondary: 60G18, 60J60

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 4 • October 1998
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