Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination

Consider a multivariate Lévy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving Lévy is from parametric family. We derive likelihood function assuming that innovation term absolutely continuous. Two examples are studied in detail: given by weak variance alpha-gamma process, which generalisation of gamma created using subordination. In former case, we give an explicit representation leading to discrete and continuous mixture, allowing for exact simulation separate function. latter show The results study demonstrate maximum numerically computed Fourier inversion can be applied accurately estimate parameters both cases.