  To extend several known centered Gaussian processes, we introduce a new
centered mixed self-similar Gaussian process called the mixed generalized
fractional Brownian motion, which could serve as a good model for a larger
class of natural phenomena. This process generalizes both the well known mixed
fractional Brownian motion introduced by Cheridito [10] and the generalized
fractional Brownian motion introduced by Zili [31]. We study its main
stochastic properties, its non-Markovian and non-stationarity characteristics
and the conditions under which it is not a semimartingale. We prove the long
range dependence properties of this process.
