Simulation of Lévy-driven Ornstein–Uhlenbeck processes with given marginal distribution

A simulation procedure for obtaining discretely observed values of Ornstein–Uhlenbeck processes with given (self-decomposable) marginal distribution is provided. The method proposed, based on inversion of the characteristic function, completely circumvents the problems encountered when trying to reproduce small jumps of Lévy processes. Error bounds for the proposed procedure are provided and its performance is numerically assessed.