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    Moments, cumulants and diagram formulae for non-linear functionals of random measures

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    Date Issued
    2008
    Author(s)
    Peccati, Giovanni
    Taqqu, Murad S.
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    Permanent Link
    https://hdl.handle.net/2144/39126
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    Published version
    Citation (published version)
    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.
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