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.
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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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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