Work

Multidimensional Stein–Malliavin calculus for the multivariate Gaussian distribution

Year: 2025

Type: article

Abstract: We develop a Stein–Malliavin calculus in order to evaluate the Wasserstein distance between the probability law of a d+p dimensional random vector (X,Y), with components regular enough in the sense of Malliavin calculus, and the probability law of the vector (Z,Y), where Z is a centered d-dimensional Gaussian vector independent of Y. We apply our theory to quantify the asymptotic independence for sequences of random vectors. We focus on some particular examples that concern the random matrices and the parameter estimators for the stochastic wave equation.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1387

Authors: Ciprian A. Tudor, Jérémy Zurcher

Institutions: Centre National de la Recherche Scientifique, Université de Lille, Laboratoire Paul Painlevé

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Agence Nationale de la Recherche, Japan Science and Technology Agency, Core Research for Evolutional Science and Technology