Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

Tomoyuki Ichiba; Ioannis Karatzas

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arXiv · 1404.4662

Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

Tomoyuki Ichiba·Ioannis Karatzas

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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.

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BibTeX RIS

Tomoyuki Ichiba, Ioannis Karatzas. 2014-07-16. Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale. https://arxiv.org/abs/1404.4662

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