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Iterated tempered stable process

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  • Soni, Ritik
  • Gajda, Janusz
  • Pathak, Ashok Kumar

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.

Suggested Citation

  • Soni, Ritik & Gajda, Janusz & Pathak, Ashok Kumar, 2025. "Iterated tempered stable process," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001440
    DOI: 10.1016/j.spl.2025.110499
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