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This work is devoted to studying complex dynamical systems under non-Gaussianfluctuations. We first estimate the Kantorovich-Rubinstein distance forsolutions of non-local Fokker-Planck equations associated with stochasticdifferential equations with non-Gaussian Levy noise. This is then applied toestablish weak convergence of the corresponding probability distributions.Furthermore, this leads to smooth approximation for non-local Fokker-Planckequations, as illustrated in an example.

Kantorovich-Rubinstein Distance and Approximation for Non-local Fokker-Planck Equations