Moments of MGOU processes and positive semidefinite matrix processes

Moment conditions for multivariate generalized Ornstein–Uhlenbeck (MGOU) processes are derived and the first and second moments are given in terms of the driving Lévy processes. In the second part of the paper a class of multivariate, positive semidefinite processes of MGOU-type is developed and suggested for use as squared volatility process in multivariate financial modeling.