Before revision:  By the way, subfractional diffusion is a candidate to describe stochastic processes with long-range dependence and non-stationarity in their increments .
After revision:  The mixed process, a linear combination between a Bm and an independent sfBm, called mixed sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding the semi-martingale property for H>3/4, is a suitable candidate to use in price fluctuation modeling, in particular for option pricing .