Seminarios

Edgeworth expansions represent the distribution of normalized sums of i.i.d. random variables as the Gaussian measure corrected by polynomial perturbations, with coefficients expressed in terms of the cumulants of the underlying distribution. 

In this talk, we present an Edgeworth expansion for a class of functionals of a Gaussian field. For an element F of the p-th Wiener chaos, using the Malliavin-Stein method and semigroup analysis, we derive bounds in the total variation distance between the distribution of F and the so-called Edgeworth development of F: a modified Gaussian measure. The bounds depend only on p and the variance of the carré-du-champ operator of F, which governs the proximity of F to the standard normal distribution.