Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative α-stable noises

作者：Zhang, Yanjie; Wang, Xiao^*; Huang, Qiao; Duan, Jinqiao; Li, Tingting

来源：APPLIED MATHEMATICAL MODELLING, 2020, 87: 711-730.

DOI：10.1016/j.apm.2020.06.031

• Finite difference scheme
• alpha-stable process
• Nonlocal Fokker-Planck equation
• Zakai equation

In this paper, we study the nonlocal Fokker-Planck equations (FPEs) associated with Levy-driven scalar stochastic dynamical systems. We first derive the Fokker-Planck equation for the case of multiplicative symmetric alpha-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.

• 单位
  华中科技大学