Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative alpha-stable noises
Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative alpha-stable noises
复制标题
具有乘法 α 稳定噪声的随机动力系统 Fokker-Planck 方程的数值分析和应用
DOI：
10.1016/j.apm.2020.06.031
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发表时间：
2020
影响因子：
5
通讯作者：
Li Tingting
中科院分区：
文献类型：
--
作者：
Zhang Yanjie;Wang Xiao;Huang Qiao;Duan Jinqiao;Li Tingting
本文研究了Lévy驱动标量随机动力系统的非局部Fokker-Planck方程。本文首先用伴随算子方法导出了乘性对称α稳定噪声的Fokker-Planck方程。然后我们构造了一个有限差分格式来模拟有界或无限域上的非局部FPE。结果表明，半离散格式满足离散最大值原理并收敛。最后通过实验验证了该方法的有效性。最后，我们将结果推广到非对称情形，并给出了一个非线性滤波问题的应用。
In this paper, we study the nonlocal Fokker-Planck equations (FPEs) associated with Lévy-driven scalar stochastic dynamical systems. We first derive the Fokker-Planck equation for the case of multiplicative symmetricα-stable noises, by the adjoint operator method. Then we construct a finite difference scheme to simulate the nonlocal FPE on either bounded or infinite domain. It is shown that the semi-discrete scheme satisfies the discrete maximum principle and converges. Some experiments are conducted to validate the numerical method. Finally, we extend the results to the asymmetric case and present an application to the nonlinear filtering problem.