Stochastic differential equations for eigenvalues and eigenvectors of a $G$-Wishart process with drift

Abstract

We propose a system of G-stochastic differential equations for the eigenvalues and eigenvectors of the $G$-Wishart process defined according to a $G$-Brownian motion matrix as in the classical case. Since we do not necessarily have the independence between the entries of the $G$-Brownian motion matrix, we assume in our model that their quadratic covariations are zero. An intermediate result, which states that the eigenvalues never collide is also obtained. This extends Bru’s results obtained for the classical Wishart process (1989).