Abstract

We develop an extension of the Stein-Malliavin calculus which allows to measure the Wasserstein distance between the probability distributions of $ (X, Y)$ and $(Z,Y)$, where $X,Y$ are arbitrary random vectors and $ Z\sim N(0, \sigma ^{2})$ is independent of $Y$. We apply this method to study the asymptotic independence for sequences of random vectors with a particular focus on the case of some estimators for some parameters of SPDEs.