Stochastic differential equations for random matrices processes in the nonlinear framework

Abstract

In this paper, we investigate the processes of eigenvalues and eigenvectors of a symmetric matrix valued process $X_{t}$, where $X_{t}$ is the solution of a general SDE driven by a $G$-Brownian motion matrix. Stochastic differential equations of these processes are given. This extends results obtained by P. Graczyk and J. Malecki in [Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503].