Gamma limits and U-statistics on the Poisson space
Probability
2013-09-16 v1
Abstract
Using Stein's method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence of multiple Wiener-Ito stochastic integrals with respect to a compensated Poisson measure converges to a Gamma distribution. As an illustration, we present a quantitative version and a non-central extension of a classical theorem by de Jong in the case of degenerate U-statistics of order two. Several multidimensional extensions, in particular allowing for mixed or hybrid limit theorems, are also provided.
Cite
@article{arxiv.1301.7289,
title = {Gamma limits and U-statistics on the Poisson space},
author = {Giovanni Peccati and Christoph Thaele},
journal= {arXiv preprint arXiv:1301.7289},
year = {2013}
}