  We propose a new approach to describe the effective microscopic dynamics of
(power-law) nonlinear Fokker-Planck equations. Our formalism is based on a
nonextensive generalization of the Wiener process. This allow us to obtain, in
addition to significant physical insights, several analytical results with
great simplicity. Indeed, we obtain analytical solutions for a nonextensive
version of Brownian free-particle and Ornstein-Uhlenbeck process, and explain
anomalous diffusive behaviours in terms of memory effects in a nonextensive
generalization of Gaussian white noise. Finally, we apply the develop formalism
to model thermal noise in electric circuits.
