On the Generalized Fractional Brownian Motion

Abstract

The generalized fractional Brownion motion (gfBm) is a new extension of both fractional and sub-fractional Brownian motions, introduced very recently. We show that this process could serve to obtain new models, better than those constructed from fractional and sub-fractional Brownian motions, permitting to take the level of correlation between the increments of the studied phenomenon into account. We also expand explicitly this process, we study the rate of convergence of the obtained expansion and, we apply our result to get a computer generation of some gfBm sample paths. In particular we present some sample paths of the even and odd parts of the fractional Brownian motion.