ON THE GENERALIZED MIXED FRACTIONAL BROWNIAN MOTION TIME CHANGED BY INVERSE α-STABLE SUBORDINATOR

Time-changed stochastic processes have attracted much attention and wide interest due to their extensive applications, especially in financial time series, network traffic, biology, and physics.This paper pays attention to a fractional stochastic process, defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst indices called the generalized mixed fractional Brownian motion, which is a Gaussian process with stationary increments exhibit long-range dependence controlled by the Hurst indices.We prove that under some conditions on the Hurst indices, the generalized mixed fractional Brownian motion time changed by inverse -stable subordinator exhibits long-range dependence property.As application, we deduce that the mixed fractional Brownian motion of Hurst index H has long-range dependence for all H > 1/2.