Skorohod-reflection of Brownian Paths and BES^3
Probability
2019-05-20 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0711.0631,
title = {Skorohod-reflection of Brownian Paths and BES^3},
author = {Balint Toth and Balint Veto},
journal= {arXiv preprint arXiv:0711.0631},
year = {2019}
}
Comments
7 pages, no figures