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.

中文翻译：

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Gamma 相关 Ornstein-Uhlenbeck 过程及其模拟*

我们研究了两个广义 Ornstein-Uhlenbeck (OU) 过程的分布特性，它们的平稳分布分别是伽马定律和双边伽马定律。所述分布与自分解伽马定律和双边伽马定律有关，它们的密度和特征函数在这里以封闭形式给出。用于精确生成此类过程的算法的优点是明显快于文献中可用的算法，因此适用于实时模拟。