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

Giovanni Peccati (1) , Murad Taqqu (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 Department of Mathematics and Statistics [Boston]

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 Möbius 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.

Mots clés: Random Measures; Central Limit Theorems; Cumulants; Diagonal measures; Diagram formulae; Gaussian fields; M\"{o}bius function; Moments; Multiple integrals; Partitions; Poisson measures; Random Measures.

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Giovanni Peccati, Murad Taqqu. Moments, cumulants and diagram formulae for non-linear functionals of random measures. 2008. ⟨hal-00338132⟩