2004/12/17 by Jean-Christophe Breton, Breton, J. C., Christian Houdré +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E07 #60F99 #60G57 #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.math/0412346
openalex publication_date 2004/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.