We derive an explicit representation for the transition law of a p-tempered \(\alpha \)-stable process of Ornstein–Uhlenbeck-type and use it to develop a methodology for simulation. Our results apply in both the univariate and multivariate cases. Special attention is given to the case where \(p\le \alpha \), which is more complicated and requires developing the new class of so-called incomplete gamma distributions.

中文翻译：

---

关于p调温$$ \ alpha $$α-稳定OU过程的转移定律

我们为Ornstein–Uhlenbeck型的p调温\（\ alpha \）稳定过程的跃迁定律导出了一个显式表示，并使用它来开发一种仿真方法。我们的结果适用于单变量和多变量情况。特别注意\（ple \ alpha \）的情况，它更复杂并且需要开发新的一类所谓的不完全伽马分布。