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 | |
| 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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