Stochastic Differential Equations for Eigenvalues and Eigenvectors of a G-Wishart Process with Drift

We propose a system of G-stochastic differential equations for the eigenvalues and eigenvectors of a 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 that, in our model, their quadratic covariations are equal to 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 in 1989.