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Séminaire de Probabilités XLIX pp 475–494Cite as

On Martingale Chaoses

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Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,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.

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Acknowledgements

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

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Centre, Bangalore, India

    B. Rajeev

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  1. B. Rajeev
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Correspondence to B. Rajeev .

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Editors and Affiliations

  1. Laboratoire de Mathématiques de Versailles, Université Versailles Saint-Quentin, Versailles, France

    Catherine Donati-Martin

  2. Institut Elie Cartan de Lorraine, Vandoeuvre-les-Nancy, France

    Antoine Lejay

  3. Laboratoire de Mathématiques de Versailles, Université Versailles Saint-Quentin, Versailles, France

    Alain Rouault

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Rajeev, B. (2018). On Martingale Chaoses. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIX. Lecture Notes in Mathematics(), vol 2215. Springer, Cham. https://doi.org/10.1007/978-3-319-92420-5_13

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