G. KANIADAKIS, P. QUARATI and A. M. SCARFONE
Generalized Brownian motion and anomalous diffusion
Received: 20 December 2000
Mathematics Subject Classification (2000): 82C31 - 82C05
Abstract: In the present contribution we consider a microscopic process described by a Langevin equation with multiplicative noise which defines a generalized Brownian motion. The associated macroscopic process is described by a linear Fokker - Planck equation with non constant coefficients.For this equation we obtain a class of solutions describing time-dependent Tsallis statistical distribution. We demonstrate that these time dependent distributions are also solutions of the standard nonlinear porous media diffusion equation.