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A note on integral representations of the Skorokhod map

Published online by Cambridge University Press:  24 March 2016

Patrick Buckingham,
Brian Fralix and
Offer Kella
Patrick Buckingham
Affiliation:
Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634-0975, USA.Email address: pbuckin@clemson.edu
Brian Fralix*
Affiliation:
Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634-0975, USA.
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Jerusalem, 91905, Israel. Email address: offer.kella@huji.ac.il
*
*** Email address: bfralix@clemson.edu
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Abstract

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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 mapregulator mapSkorokhod problem

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016, pp. 293 - 298
Copyright
Copyright © Applied Probability Trust 2016 

References

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