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

A time-changed fractional mixed fractional Brownian motion by inverse -stable subordinator with index (0, 1) is an iterated process(a, b) constructed as the superposition of fractional mixed fractional Brownian motion N H 1 H 2 (a, b) and an independent inverse -stable subordinator T .In this paper we prove that the process L H 1 H 2 T (a, b) exhibit long range dependence property under some condition on the Hirst indices H 1 and H 2 of tow independents fractional Brownian motions.