Reflecting thoughts

Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The purpose of this note is to provide an equivalent definition and an alternative proof of uniqueness of the one-dimensional reflection map which is more a direct derivation that structurally leads to the form of the map when it exists, does not involve integration (neither in the definition nor in the proof) and for which no assumptions on the driving process is needed. Also, it is argued that, with the proposed definition, the reflection map exists provided that the driving process is lower semicontinuous from the right, but is not necessarily right continuous and does not necessarily have left limits. These ideas are then easily extended to the multidimensional case.

Original languageAmerican English
Pages (from-to)1808-1811
Number of pages4
JournalStatistics and Probability Letters
Issue number16
StatePublished - 1 Oct 2006

Bibliographical note

Funding Information:
Supported in part by Grant 819/03 from the Israel Science Foundation.


  • Local time
  • Reflection mapping
  • Regulator
  • Skorohod problem


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