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 .
