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On an extension of the Hilbertian central limit theorem to Dirichlet forms

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  • Christophe Chorro

    (CERMSEM et CERMICS)

Abstract

In a recent paper, Bouleau provides a new tool, based on the language of Dirichlet forms, to study the errors propagation and reinforce the historical approach of Gauss. As the classical central limit theorem is a theoric justification of the employment of normal laws in statistics, the aim of this article is to underline the importance of certain classes of error structures by asymptotic arguments. Thus, we extend the notions of independence and convergence in distribution for random variables in order to prove a refinement of the hilbertian central limit theorem that highlights the fundamental role of the error structures of the Ornstein-Ulhenbeck type

Suggested Citation

  • Christophe Chorro, 2004. "On an extension of the Hilbertian central limit theorem to Dirichlet forms," Cahiers de la Maison des Sciences Economiques b04080, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04080
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04080.pdf
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    References listed on IDEAS

    as
    1. Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 115-134, January.
    2. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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    Cited by:

    1. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Cahiers de la Maison des Sciences Economiques b05036, Université Panthéon-Sorbonne (Paris 1).
    2. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Post-Print halshs-00194673, HAL.

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    More about this item

    Keywords

    Error; sensitivity; Dirichlet forms; squared field operator; vectorial domain; central limit theorem;
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