A generalization of the classical Ornstein Uhlenbeck diffusion process including some deterministic time dependent functions in the infinitesimal moments is considered. The inference based on discrete sampling in time is provided by means of an iterative procedure that, in each step, combines the classical maximum likelihood estimation and a generalized method of moments. The validity of the suggested procedure is evaluated via a simulation study by considering several infinitesimal moments for the Ornstein Uhlenbeck type process and taking different sample size. Finally, an application to PM10 daily concentration in Turin metropolitan area in Italy is discussed.

中文翻译：

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推断时间非齐次 Ornstein Uhlenbeck 型随机过程

考虑了经典 Ornstein Uhlenbeck 扩散过程的推广，包括无穷小矩中的一些确定性时间相关函数。基于时间离散采样的推理是通过迭代过程提供的，该过程在每个步骤中都结合了经典的最大似然估计和广义矩方法。通过考虑 Ornstein Uhlenbeck 型过程的几个无穷小矩并采用不同的样本大小，通过模拟研究评估建议程序的有效性。最后，讨论了在意大利都灵市区 PM10 日浓度的应用。