Wiener Chaos: Moments, Cumulants and Diagrams

This is a book about combinatorial structures related to the law of random variables belonging to a so-called Wiener chaos, that is, to a space of multiple stochastic integrals (of a given fixed order) associated with some infinitely divisible random measure. The combinatorial structures involved are those of lattices of partitions of finite sets, over which we define incidence algebras, Möbius functions and associated inversion formulae. As discussed in the text, this combinatorial standpoint ...