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

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arxiv 2109.02493 v1 pith:RRVG7V3Y submitted 2021-09-06 math.PR math.DS

Ao Zhang , Jinqiao Duan This is my paper · ORCID
classification math.PRmath.DS
keywords equationsfokker-plancknon-localapproximationdistancekantorovich-rubinsteinnon-gaussianapplied
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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 Levy 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.

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