Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes

Abstract The exact pathwise simulation of multidimensional Ornstein–Uhlenbeck processes is considered. We propose two procedures that allow the exact pathwise simulation of this type of processes and, simultaneously, the generation of the underlying Wiener trajectories from the same source of randomness. This is particularly important when both processes are system-components in larger stochastic models, for which the study of pathwise dynamics is required.