Dimension Free and Infinite Variance Tail Estimates on Poisson Space

• Autores: Jean-Christophe Breton, Christian Houdré, Nicolas Privault
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 95, Nº. 3, 2007, págs. 151-203
• Idioma: inglés
• DOI: 10.1007/s10440-007-9084-3
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• Resumen

  • 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.