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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integral representation of Skorokhod reflection


Authors: Venkat Anantharam and Takis Konstantopoulos
Journal: Proc. Amer. Math. Soc. 139 (2011), 2227-2237
MSC (2010): Primary 60G17; Secondary 45G99, 90B05
Published electronically: January 28, 2011
MathSciNet review: 2775400
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Abstract: We show that a certain integral representation of the one-sided Skorokhod reflection of a continuous bounded variation function characterizes the reflection in that it possesses a unique maximal solution which solves the Skorokhod reflection problem.


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Additional Information

Venkat Anantharam
Affiliation: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720
Email: ananth@eecs.berkeley.edu

Takis Konstantopoulos
Affiliation: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
Email: Takis.Konstantopoulos@math.uu.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10811-6
PII: S 0002-9939(2011)10811-6
Keywords: Skorokhod reflection, sample path properties, integral representation, storage systems
Received by editor(s): May 21, 2010
Published electronically: January 28, 2011
Additional Notes: The research of the first author was supported by the ARO MURI grant W911NF-08-1-0233, Tools for the Analysis and Design of Complex Multi-Scale Networks, by the NSF grants CCF-0635372 and CNS-0910702, by Marvell Semiconductor Inc., and by the U. C. Discovery program.
The second author was supported in part by an EPSRC grant and by the Isaac Newton Institute for Mathematical Sciences.
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2011 American Mathematical Society