Linnik Lévy process and some extensions

A. Kumar, A. Maheshwari and A. Wyłomańska

Physica A: Statistical Mechanics and its Applications, 2019, vol. 529, issue C

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.

Keywords: Linnik distribution; Linnik process; Subordinated stochastic processes; Lévy density; Estimation; Simulation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:529:y:2019:i:c:s0378437119309033

DOI: 10.1016/j.physa.2019.121539

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