A note on the Markov property of stochastic processes described by nonlinear Fokker-Planck equations

摘要

We study the Markov property of processes described by generalized Fokker-Planck equations that are nonlinear with respect to probability densities such as mean field Fokker-Planck equations and Fokker-Planck equations related to generalized thermostatistics. We show that their transient solutions describe non-Markov processes. In contrast, stationary solutions can describe Markov processes. As a result, nonlinear Fokker-Planck equations can be used to model transient non-Markov processes that converge to stationary Markov processes. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 44]