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

Abstract

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.