  A new extension of the sub-fractional Brownian motion, and thus of the
Brownian motion, is introduced. It is a linear combination of a finite number
of sub-fractional Brownian motions, that we have chosen to call the mixed
sub-fractional Brownian motion. In this paper, we study some basic properties
of this process, its non-Markovian and non-stationarity characteristics, the
conditions under which it is a semimartingale, and the main features of its
sample paths. We also show that this process could serve to get a good model of
certain phenomena, taking not only the sign (like in the case of the
sub-fractional Brownian motion), but also the strength of dependence between
the increments of this phenomena into account.
