We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross–Sobolev space D1,2 of random variables with a square-integrable Malliavin derivative, we let ΓF,G≔〈DF,−DL−1G〉, where D is the Malliavin derivative operator and L−1 is the...

We consider sequences of random variables of the type $S_n= n^{-1/2} \sum_{k=1}^n f(X_k)$, $n\geq 1$, where $X=(X_k)_{k\in \Z}$ is a $d$-dimensional Gaussian process and $f: \R^d \rightarrow \R$ is a measurable function. It is known that, under certain conditions on $f$ and the covariance...

Let {Fn} be a sequence of random variables belonging to a finite sum of Wiener chaoses. Assume further that it converges in distribution towards F∞ satisfying V ar(F∞)0. Our first result is a sequential version of a theorem by Shigekawa (1980) [23]. More precisely, we prove, without...

Continuing the analysis initiated by Lachièze-Rey and Peccati (2013), we use contraction operators to study the normal approximation of random variables having the form of a U-statistic written on the points in the support of a random Poisson measure. Applications are provided to subgraph...