This paper considers discretization of the Lévy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity assumptions on the given Lévy process. Additionally, the scaling limit of a positive self-similar Markov process at small times is provided. Finally, we present an application to simulation of self-similar Lévy processes conditioned to stay positive.

中文翻译：

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正自相似马尔可夫过程的Lamperti表示的离散化

本文考虑了在严格正自相似马尔可夫过程的Lamperti表示中出现的Lévy过程的离散化。在给定的Lévy过程的某些规律性假设下，建立了所得近似值的极限定理。另外，提供了正次数自相似马尔可夫过程在小时间的缩放极限。最后，我们提出了一种用于模拟保持相似的自相似Lévy过程的应用程序。