Gamma Related Ornstein-Uhlenbeck Processes and their Simulation
arXiv:2003.08810 · doi:10.1080/00949655.2020.1842408
Abstract
We investigate the distributional properties of two generalized Ornstein-Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to the self-decomposable gamma and bilateral gamma laws, and their densities and characteristic functions are here given in closed-form. Algorithms for the exact generation of such processes are accordingly derived with the advantage of being significantly faster than those available in the literature and therefore suitable for real-time simulations.
27 pages, 2 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:1908.03137