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Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises

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  • Wang, Xiao
  • Duan, Jinqiao
  • Li, Xiaofan
  • Luan, Yuanchao

Abstract

The mean exit time and escape probability are deterministic quantities that can quantify dynamical behaviors of stochastic differential equations with non-Gaussian α-stable type Lévy motions. Both deterministic quantities are characterized by differential–integral equations (i.e., differential equations with nonlocal terms) but with different exterior conditions. A convergent numerical scheme is developed and validated for computing the mean exit time and escape probability for two-dimensional stochastic systems with rotationally symmetric α-stable type Lévy motions. The effects of drift, Gaussian noises, intensity of jump measure and domain sizes on the mean exit time are discussed. The difference between the one-dimensional and two-dimensional cases is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:282-295
    DOI: 10.1016/j.amc.2015.01.117
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    References listed on IDEAS

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    1. Xu, Yong & Feng, Jing & Li, JuanJuan & Zhang, Huiqing, 2013. "Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4739-4748.
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    Cited by:

    1. Qingyi Zhan & Zhifang Zhang & Yuhong Li, 2021. "Numerical implementation of finite-time shadowing of stochastic differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 945-960, December.
    2. Duan, Wei-Long & Zeng, Chunhua, 2017. "Signal power amplification of intracellular calcium dynamics with non-Gaussian noises and time delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 400-405.
    3. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Song, Renming, 2018. "Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 618-634.
    4. 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.
    5. Qingyi Zhan & Zhifang Zhang & Yuhong Li, 2020. "Numerical Implementation of Finite-Time Shadowing of Stochastic Differential Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1939-1957, December.

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