Exact moment scaling from multiplicative noise

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 nontrivial time dependence of the microscopic dynamics and we analytically
characterize the process evolution, possibly toward a stationary state, and the direct relationship existing
between the drift and diffusion coefficients and the time scaling of the moments.