Fractional Levy stable motion time-changed by gamma subordinator

Abstract

In this paper a new stochastic process is introduced by subordinating fractional Levy stable motion (FLSM) with gamma process. This new process incorporates stochastic volatility in the parent process FLSM. Fractional order moments, tail asymptotic, codifference and persistence of signs long-range dependence of the new process are discussed. A step-by-step procedure for simulations of sample trajectories and estimation of the parameters of the introduced process are given. Our study complements and generalizes the results available on variance-gamma process and fractional Laplace motion in various directions, which are well studied processes in literature.