Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale
Probability
2014-07-18 v3
Abstract
The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.
Keywords
Cite
@article{arxiv.1404.4662,
title = {Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale},
author = {Tomoyuki Ichiba and Ioannis Karatzas},
journal= {arXiv preprint arXiv:1404.4662},
year = {2014}
}
Comments
20 pages. typos corrected, added a remark after Proposition 2.3, simplified the last part of Example 2.2