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.
Publié le : 2004-07-05
Classification:
large deviations,
Concentration inequality,
infinite divisibility,
stable laws,
Poisson space,
Ornstein-Uhlenbeck semi-group,
quadratic Wiener functionals,
large deviations.,
(AMS) 60F99 ; 60E07 ; 60G57.,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00348285,
author = {Breton, J. C. and Houdr\'e, C. and Privault, N.},
title = {Dimension free and infinite variance tail estimates on Poisson space},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00348285}
}
Breton, J. C.; Houdré, C.; Privault, N. Dimension free and infinite variance tail estimates on Poisson space. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00348285/