Deviation Inequalities: an Approach via Covariance Representations

 

Christian Houdré   Nicolas Privault
School of Mathematics   Département de Mathématiques
Georgia Institue of Technology   Université de la Rochelle
Atlanta, Ga 30332   17042 La Rochelle Cedex 1
USA   France

 

Abstract:

Various deviation inequalities are obtained for functionals on Wiener space, Poisson space or more generally for normal martingales. The method is based on covariance identities obtained via the chaotic representation property, and extends to the binomial process and to the infinite discrete cube {-1,1}.

Key words: Deviation inequalities, covariance identities, chaotic representation property, Clark formula.
Mathematics Subject Classification (1991): 62E20, 60H07, 60G44, 60G57.

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