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This survey provides a unified discussion of multiple integrals, moments,cumulants and diagram formulae associated with functionals of completely randommeasures. Our approach is combinatorial, as it is based on the algebraicformalism of partition lattices and M\"obius functions. Gaussian and Poissonmeasures are treated in great detail. We also present several combinatorialinterpretations of some recent CLTs involving sequences of random variablesbelonging to a fixed Wiener chaos.

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