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An identity in distribution due to F. Knight for Brownian motion is extended in two different ways: firstly by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion, and secondly 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 Ito's law of Brownian excursions, due to D. Williams and J.-M. 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.

Details

Title
Random Brownian Scaling Identities and Splicing of Bessel Processes
Creator
Pitman, Jim, Author
Yor, Marc, Author
Published
Statistics Department, University of California, Berkeley, University of California at Berkeley, Berkeley, California, Sep 1997
Full Collection Name
Statistics Technical Reports
Other Identifiers
490
Type
Text
Format
technical reports
Archive
Mathematics Statistics Library
Note
Ann. Prob. 26, 1683-1702 (1998)
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