A note on integral representations of the Skorokhod map

Patrick Buckingham; Brian Fralix; Offer Kella

doi:10.1017/jpr.2015.25

A note on integral representations of the Skorokhod map

Patrick Buckingham, Brian Fralix, Offer Kella

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We present a very short derivation of the integral representation of the two-sided Skorokhod reflection Z of a continuous function X of bounded variation, which is a generalization of the integral representation of the one-sided map featured in Anantharam and Konstantopoulos (2011) and Konstantopoulos et al. (1996). We also show that Z satisfies a simpler integral representation when additional conditions are imposed on X. Keywords: Reflection map; regulator map; Skorokhod problem.

Original language	English
Pages (from-to)	293-298
Number of pages	6
Journal	Journal of Applied Probability
Volume	53
Issue number	1
DOIs	https://doi.org/10.1017/jpr.2015.25
State	Published - Mar 2016

Bibliographical note

Funding Information:
B. Fralix was supported by the National Science Foundation (grant no. CMMI-1435261). O. Kella was supported by the Israel Science Foundation (grant no. 1462/13) and the Vigevani Chair in Statistics.

Publisher Copyright:
© Applied Probability Trust 2016.

Keywords

Reflection map
Regulator map
Skorokhod problem

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10.1017/jpr.2015.25

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A note on integral representations of the Skorokhod map

Abstract

Bibliographical note

Keywords

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