Random Brownian Scaling Identities and Splicing of Bessel Processes
نویسنده
چکیده
An identity in distribution due to F. Knight for Brownian motion is extended in two di erent ways: rstly by replacing the supremum of a re ecting Brownian motion by the range of an unre ected Brownian motion, and secondly by replacing the re ecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The rst extension is related to two di erent constructions of Itô'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.
منابع مشابه
Random Brownian Scaling Identities
An identity in distribution due to F. Knight for Brownian motion is extended in two diierent ways: rstly by replacing the supremum of a reeecting Brownian motion by the range of an unreeected Brownian motion, and secondly by replacing the reeecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...
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