A note on integral representations of the Skorokhod map

Patrick Buckingham; Brian Fralix; Offer Kella

doi:https://doi.org/10.1017/jpr.2015.25

A note on integral representations of the Skorokhod map

Patrick Buckingham, Brian Fralix, Offer Kella

Department of Statistics

The Hebrew University of Jerusalem

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

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

Keywords

Reflection map
Regulator map
Skorokhod problem

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
General Mathematics

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https://doi.org/10.1017/jpr.2015.25

Cite this

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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.",

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author = "Patrick Buckingham and Brian Fralix and Offer Kella",

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AU - Fralix, Brian

AU - Kella, Offer

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Y1 - 2016/3

N2 - 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.

AB - 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.

KW - Reflection map

KW - Regulator map

KW - Skorokhod problem

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M3 - مقالة

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EP - 298

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 1

ER -

A note on integral representations of the Skorokhod map

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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