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Symplectic numerical integration for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus

Author

Listed:
  • Zhan, Qingyi
  • Duan, Jinqiao
  • Li, Xiaofan
  • Li, Yuhong

Abstract

In this paper, we propose a symplectic numerical integration method for a class of Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus. We first construct a general symplectic Euler scheme for these equations, then we prove its convergence. In addition, we provide realizable numerical implementations for the proposed symplectic Euler scheme in detail. Some numerical experiments are conducted to demonstrate the effectiveness and superiority of the proposed method by the simulations of its orbits, Hamiltonian and convergence order over a long time interval. The results show the applicability of the methods considered.

Suggested Citation

  • Zhan, Qingyi & Duan, Jinqiao & Li, Xiaofan & Li, Yuhong, 2024. "Symplectic numerical integration for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 420-439.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:420-439
    DOI: 10.1016/j.matcom.2023.08.012
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    References listed on IDEAS

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    1. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Luan, Yuanchao, 2015. "Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 282-295.
    2. Tetsuya Misawa, 2010. "Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, August.
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