Iterated tempered stable process

Ritik Soni, Janusz Gajda and Ashok Kumar Pathak

Statistics & Probability Letters, 2025, vol. 226, issue C

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.

Keywords: Tempered stable subordinators; Laplace transform; Fractional differential equations; Mean square displacement; Sample paths (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110499

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