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Positivity

, Volume 18, Issue 3, pp 425–437 | Cite as

On the decompositions of \(T\)-quasi-martingales on Riesz spaces

  • Jessica J. Vardy
  • Bruce A. WatsonEmail author
Article

Abstract

The concept of a quasi-martingale is generalised to the Riesz space setting. Here we show that a quasi-martingale can be decomposed into the sum of a martingale and a quasi-potential. If, in addition, the quasi-martingale and its filtration are right continuous we show that the quasi-martingale can decomposed into the sum of a right continuous martingale and the difference of two positive right continuous potentials. The approach is measure-free and relies entirely on the order structure of Riesz spaces.

Keywords

Riesz space Conditional expectation Quasi-martingale 

Mathematics Subject Classification (2000)

46A40 47B60 60G20 60G48 

Notes

Acknowledgments

We thank Professor J.J. Grobler and the referee for their valuable suggestions and comments.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.School of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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