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.
Publié le : 1998-10-14
Classification:
Brownian bridge,
Brownian excursion,
Brownian scaling,
path transformation,
Williams' decomposition,
local time,
Bessel process,
range process,
60J65,
60G18,
60J60
@article{1022855878,
author = {Pitman, Jim and Yor, Marc},
title = {Random Brownian scaling identities and splicing of Bessel
processes},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1683-1702},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855878}
}
Pitman, Jim; Yor, Marc. Random Brownian scaling identities and splicing of Bessel
processes. Ann. Probab., Tome 26 (1998) no. 1, pp. 1683-1702. http://gdmltest.u-ga.fr/item/1022855878/