Stochastic differential equations for orthogonal eigenvectors of (G,ε)-Wishart process related to multivariate G-fractional Brownian motion

Abstract

In the present paper, we introduce a new process called multivariate G-fractional Brownian motion (B_{t}^{H}) where the Hurst parameter H is a diagonal matrix. Moreover, we give an approximation (R_{t}^{ε}) of Riemann-Liouville process of (B_{t}^{H}) by G-Itô's processes. Then we give stochastic differential equations for orthogonal eigenvectors of (G,ε)-Wishart fractional process defined by R_{t}^{ε}(R_{t}^{ε})^{∗}, which has 0 and |R_{t}^{ε}|² as eigenvalues. An intermediate asymptotic comparison result concerning the eigenvalue |R_{t}^{ε}|² is also obtained