Skorohod-reflection of Brownian Paths and BES^3

Details Skorohod-reflection of Brownian Paths and BES^3 Skorohod-reflection of Brownian Paths and BES^3

2007-11-05

arxiv.org/abs/0711.0631v1

Mathematics

Probability

7 pages, no figures

Scientific paper

Let B(t), X(t) and Y(t) be independent standard 1d Borwnian motions. Define X^+(t) and Y^-(t) as the trajectories of the processes X(t) and Y(t) pushed upwards and, respectively, downwards by B(t), according to Skorohod-reflection. In a recent paper, Jon Warren proves inter alia that Z(t):= X^+(t)-Y^-(t) is a three-dimensional Bessel-process. In this note, we present an alternative, elementary proof of this fact.

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