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Dimension Free and Infinite Variance Tail Estimates on Poisson Space

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Abstract

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including Lévy’s stochastic area and the square norm of Brownian paths. In the infinite variance case, various tail estimates such as stable ones are also presented.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Poitiers, Téléport 2-BP30179, 86962, Chasseneuil, France

    Nicolas Privault

  2. Laboratoire de Mathématiques, Université de la Rochelle, Avenue Michel Crépeau, 17042, La Rochelle, France

    Jean-Christophe Breton

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Christian Houdré

Authors
  1. Jean-Christophe Breton
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  2. Christian Houdré
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  3. Nicolas Privault
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Correspondence to Nicolas Privault.

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Breton, JC., Houdré, C. & Privault, N. Dimension Free and Infinite Variance Tail Estimates on Poisson Space. Acta Appl Math 95, 151–203 (2007). https://doi.org/10.1007/s10440-007-9084-3

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  • DOI: https://doi.org/10.1007/s10440-007-9084-3

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