Tempered Mittag-Leffler Lévy processes |
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| Authors: | A Kumar N S Upadhye J Gajda |
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| Institution: | 1. Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India;2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India;3. Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroc?aw University of Science and Technology, Wybrze?e Wyspiańskiego 27, Wroc?aw, Poland |
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| 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. |
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| Keywords: | Lévy density Mittag-Leffler distribution subordinated stochastic processes |
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