Abstract:
In the literature, the Linnik, Mittag-Leffler, Laplace and asymmetric Laplace distributions
are the most known examples of geometric stable distributions. The geometric stable
distributions are especially useful in the modeling of leptokurtic data with heavy-tailed
behavior. They have found many interesting applications in the modeling of several
physical phenomena and financial time-series. In this paper, we define the Linnik
Lévy process (LLP) through the subordination of symmetric stable Lévy motion with
gamma process. We discuss main properties of LLP like probability density function, Lévy
measure and asymptotic forms of marginal densities. We also consider the governing
fractional-type Fokker–Planck equation. To show practical applications, we simulate the
sample paths of the introduced process. Moreover, we give a step-by-step procedure
of the parameters estimation and calibrate the parameters of the LLP with the Arconic
Inc equity data taken from Yahoo finance. Further, some extensions of the introduced
process are also discussed.
