Moments, cumulants and diagram formulae for non-linear functionals of random measures
arXiv:0811.1726
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 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.
Survey, preliminary draft. 104 pages. 30 Figures
References in corpus (5)
- Central limit theorems for sequences of multiple stochastic integrals
- Renormalized self-intersection local time for fractional Brownian motion
- Noncentral convergence of multiple integrals
- Central limit theorems for double Poisson integrals
- Central and non-central limit theorems for weighted power variations of fractional Brownian motion