  For a general class of diffusion processes with multiplicative noise,
describing a variety of physical as well as financial phenomena, mostly typical
of complex systems, we obtain the analytical solution for the moments at all
times. We allow for a non trivial time dependence of the microscopic dynamics
and we analytically characterize the process evolution, possibly towards a
stationary state, and the direct relationship existing between the drift and
diffusion coefficients and the time scaling of the moments.
