Moments, cumulants and diagram formulae for non-linear functionals of random measures
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Published version
Date
2008
DOI
Authors
Peccati, Giovanni
Taqqu, Murad S.
Version
Published version
OA Version
Citation
Giovanni Peccati, Murad S Taqqu. 2008. "Moments, cumulants and diagram formulae for non-linear functionals of random measures." arXiv.
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.