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

In this paper, we study some aspects on random analysis on the Léevy 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.