Iterated tempered stable process

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-07-08 DOI:10.1016/j.spl.2025.110499

Ritik Soni , Janusz Gajda , Ashok Kumar Pathak

引用次数: 0

Abstract

In this paper, we introduce the iterated tempered stable process (ITSS) by subordinating a tempered

α

-stable subordinator (TSS) with another independent TSS. The proposed model generalizes several important Lévy models studied in Gajda and Wylomańska (2013), Gajda et al., (2019), and Kumar et al., (2017). We derive its distributional properties and explore its connections with fractional calculus. We present sample paths of the ITSS for different parameters and observe perfect agreement between theoretical and empirical Laplace transform estimated from the simulated samples. The tail behavior and the fractional order moments of the ITSS are also discussed. We define the first passage time of the ITSS and study its tail behavior. Additionally, we present a time-changed TSS model and highlight its connection to tempered fractional differential equations.

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迭代回火稳定过程

本文介绍了一个α-稳定的回火子过程（TSS）与另一个独立的TSS从属的迭代回火稳定过程（ITSS）。本文提出的模型概括了Gajda和Wylomańska（2013）、Gajda等人（2019）和Kumar等人（2017）研究过的几个重要的lsamvy模型。我们推导了它的分布性质，并探讨了它与分数阶微积分的联系。我们给出了不同参数下ITSS的样本路径，并观察到由模拟样本估计的理论和经验拉普拉斯变换之间的完美一致性。讨论了ITSS的尾部特性和分数阶矩。我们定义了ITSS的首次通过时间，并研究了它的尾部行为。此外，我们提出了一个时变的TSS模型，并强调了它与缓和分数阶微分方程的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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