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Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion

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  • Wang, Xiao
  • Duan, Jinqiao
  • Li, Xiaofan
  • Song, Renming

Abstract

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent numerical method for the mean first exit time and escape probability for stochastic systems with an asymmetric Lévy motion, and analyze the properties of the solutions of the nonlocal equations. The discretized equation has Toeplitz structure that enables utilization of fast Fourier transform in numerical simulations. We also investigate the effects of different system factors on the mean exit time and escape probability, including the skewness parameter, the size of the domain, the drift term and the intensity of Gaussian and non-Gaussian noises. We find that the behavior of the mean exit time and the escape probability has dramatic difference at the boundary of the domain when the index of stability crosses the critical value of one.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:618-634
    DOI: 10.1016/j.amc.2018.05.038
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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. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
    3. Koren, T. & Chechkin, A.V. & Klafter, J., 2007. "On the first passage time and leapover properties of Lévy motions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 10-22.
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    Cited by:

    1. Mao, Yicheng & Liu, Xianbin, 2024. "A mesh-free generalized method for stochastic stability analysis: Mean exit time and escape probability of dynamical systems driven by Gaussian white noise and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    2. Song, Yi & Xu, Wei & Wei, Wei & Niu, Lizhi, 2023. "Dynamical transition of phenotypic states in breast cancer system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
    3. Song, Yi & Xu, Wei, 2021. "Asymmetric Lévy noise changed stability in a gene transcriptional regulatory system," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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