Higher-order Stein kernels for Gaussian approximation

Max Fathi (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics on the space of probability measures and prove new functional inequalities involving them. As an application , we obtain new explicit improved rates of convergence in the classical multidimensional CLT under higher moment and regularity assumptions.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Max Fathi. Higher-order Stein kernels for Gaussian approximation. Studia Mathematica, In press. ⟨hal-02350138⟩