Abstract
In this article, we introduce generalized Mittag-Leffler Lévy (GMLL) process. GMLL distribution is represented as a general Lévy subordinator delayed by a gamma process. We show various properties of this new process like it’s corresponding Lévy density function and the so-called long-range dependence property. We provide also an explicit representation for the cumulative density function (CDF) for such process which can be an inspiration for construction of various versions of the GMLL processes. Moreover we establish Fokker-Planck type equation for its one dimensional probability density functions (PDF). Our construction will allow us to link GMLL process to the first passage time of the Lévy subordinator.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have