A Hopf-algebraic approach to cumulants-moments relations and Wick polynomials
Résumé
We present a different approach to classical definitions and results on cumulant-moment relations and Wick polynomials, which is based on extensive use of convolution products of linear functionals on a coalgebra. It allows, in particular, to understand the construction of Wick polynomials as the result of a Hopf algebra deformation under the action of linear automorphisms induced by multivariate moments associated to an arbitrary family of random variables with moments at all orders.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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