Fokker–Planck equations for stochastic dynamical systems with symmetric Lévy motions

Ting Gao, Jinqiao Duan and Xiaofan Li

Applied Mathematics and Computation, 2016, vol. 278, issue C, 1-20

Abstract: The Fokker–Planck equations for stochastic dynamical systems, with non-Gaussian α-stable symmetric Lévy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian fluctuations. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker–Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. It is validated against a known exact solution and the numerical solutions obtained by using other methods. The numerical results for two prototypical stochastic systems, the Ornstein–Uhlenbeck system and the double-well system are shown.

Keywords: Non-Gaussian noise; α-stable symmetric Lévy motion; Fractional Laplacian operator; Fokker–Planck equation; Maximum principle; Toeplitz matrix (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:278:y:2016:i:c:p:1-20

DOI: 10.1016/j.amc.2016.01.010

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