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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


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.


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

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

Primary: 60J65
Secondary: 60G18 , 60J60

Keywords: Bessel process , Brownian bridge , Brownian excursion , Brownian scaling , Local time , path transformation , range process , Williams' decomposition

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • October 1998
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