Dimension free and infinite variance tail estimates on Poisson space

Details Dimension free and infinite variance tail estimates on Poisson space Dimension free and infinite variance tail estimates on Poisson space

2004-12-17

arxiv.org/abs/math/0412346v1

Mathematics

Probability

61 pages

Scientific paper

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 L\'evy'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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