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A short proof of decomposition of strongly reduced martingales

Théorie des Martingales

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1709)

Abstract

A short proof of the following theorem is given: If M is a martingale, T>0 is a stopping time, M=M T and is bounded, then M is a sum of a BMO (and, thus, square-integrable) martingale and a martingale of integrable variation.

AMS Subject Classification

  • 60 G 44
  • Key words and phrases
  • martingale
  • decomposition

The work of the first author was supported in part by KBN Grant 2 P03A 01813. This article was written in part when the first author was visiting the Department of Mathematics, University of Louisville, Kentucky, USA.

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References

  • [Me] P.A. Meyer, Un cours sur les integrales stochastiques, Séminaire de Probabilités X, Lecture Notes in Mathematics 511, Berlin, Heidelberg, New York 1976.

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© 1999 Springer-Verlag

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Morayne, M., Tabisz, K. (1999). A short proof of decomposition of strongly reduced martingales. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXIII. Lecture Notes in Mathematics, vol 1709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096523

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  • DOI: https://doi.org/10.1007/BFb0096523

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66342-3

  • Online ISBN: 978-3-540-48407-3

  • eBook Packages: Springer Book Archive