Kantorovich–Rubinstein distance and approximation for non-local Fokker–Planck equations

Abstract

This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich–Rubinstein distance for solutions of non-local Fokker–Planck equations associated with stochastic differential equations with non-Gaussian Lévy noise. This is then applied to establish weak convergence of the corresponding probability distributions. Furthermore, this leads to smooth approximation for non-local Fokker–Planck equations, as illustrated in an example.