Moments, cumulants and diagram formulae for non-linear functionals of random measures
Probability
2008-11-12 v1 Combinatorics
Abstract
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of partition lattices and M\"obius functions. Gaussian and Poisson measures are treated in great detail. We also present several combinatorial interpretations of some recent CLTs involving sequences of random variables belonging to a fixed Wiener chaos.
Keywords
Cite
@article{arxiv.0811.1726,
title = {Moments, cumulants and diagram formulae for non-linear functionals of random measures},
author = {Giovanni Peccati and Murad S. Taqqu},
journal= {arXiv preprint arXiv:0811.1726},
year = {2008}
}
Comments
Survey, preliminary draft. 104 pages. 30 Figures