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Tempered Mittag-Leffler Lévy processes

Author

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  • A. Kumar
  • N. S. Upadhye
  • A. Wyłomańska
  • J. Gajda

Abstract

In this article, we introduce tempered Mittag-Leffler Lévy processes (TMLLP). TMLLP is represented as tempered stable subordinator delayed by a gamma process. Its probability density function and Lévy density are obtained in terms of infinite series and Mittag-Leffler function, respectively. Asymptotic forms of the tails and moments are given. A step-by-step procedure of the parameters estimation and simulation of sample paths is given. We also provide main results available for Mittag-Leffler Lévy processes (MLLP) and some extensions which are not available in a collective way in a single article. Our results generalize and complement the results available on Mittag-Leffler distribution and MLLP in several directions. Further, the asymptotic forms of the moments of the first-exit times of the TMLLP are also discussed.

Suggested Citation

  • A. Kumar & N. S. Upadhye & A. Wyłomańska & J. Gajda, 2019. "Tempered Mittag-Leffler Lévy processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(2), pages 396-411, January.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:2:p:396-411
    DOI: 10.1080/03610926.2017.1410719
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    Cited by:

    1. Lin, Lifeng & He, Minyue & Wang, Huiqi, 2022. "Collective resonant behaviors in two coupled fluctuating-mass oscillators with tempered Mittag-Leffler memory kernel," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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