Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem

Thomas Gallouët, Guillaume Mijoule, Yvik Swan

Consider the multivariate Stein equation $\Delta f-x\cdot \nabla f=h(x)-Eh(Z)$, where $Z$ is a standard $d$-dimensional Gaussian random vector, and let $f\_h$ be the solution give…