Elements of Randoms Analysis about the Gamma Generalized Hyperbolic Distribution Levy Stochastic Process

TL;DR

This paper investigates the properties of Levy processes with generalized hyperbolic distribution margins, focusing on variation measures and graphical path representations, and compares them to Brownian motion.

Contribution

It provides new insights into the variation properties of gamma generalized hyperbolic Levy processes and introduces an empirical method for visualizing their paths.

Findings

Boundedness of total variations established

Quadratic variations analyzed

Graphical path representations developed

Abstract

In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations and the quadratic variations. Next we give an empirical construction that enables the graphical representation of the paths of such stochastic processes. Comparisons with the Brownian motions are considered.