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, 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 property controlled by the Hurst indices. We prove that under some condition on the Hurst indices the generalized mixed fractional Brownian motion time changed by inverse α-stable subordinator is of a long-range dependence property. As application we deduce that the mixed fractional Brownian motion of Hurst index H has long range dependence property for all H > (Formula presented).