Tempered Mittag-Leffler Lévy processes

Anjani Kumar, N. S. Upadhye, A. Wyłomańska and J. Gajda

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 2, 396-411

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.

Date: 2019
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DOI: 10.1080/03610926.2017.1410719

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