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On Martingale Chaoses

  • B. Rajeev
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2215)

Abstract

We extend Wiener’s notion of ‘homogeneous’ chaos expansion of Brownian functionals to functionals of a class of continuous martingales via a notion of iterated stochastic integral for such martingales. We impose a condition of ‘homogeneity’ on the previsible sigma field of such martingales and show that under this condition the notions of purity, chaos representation property and the predictable representation property all coincide.

Keywords

Martingale representation Stochastic integral representation Chaos expansion CRP PRP Pure martingales 

Mathematics Subject Classification (2000)

Primary 60H10 60H15; Secondary 60J60 35K15 

Notes

Acknowledgements

The author would like to thank Michel Émery for extensive discussions over e-mail.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Statistics and Mathematics UnitIndian Statistical Institute, Bangalore CentreBangaloreIndia

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