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On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations

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  • Li, Xiuping
  • Cao, Wanrong

Abstract

The asymptotic mean-square stability of two-step Maruyama methods is considered for nonlinear neutral stochastic differential equations with constant time delay (NSDDEs). Under the one-sided Lipschitz condition and the linear growth condition, it is proved that a family of implicit two-step Maruyama methods can preserve the stability of the analytic solution in mean-square sense. Numerical results for both a nonlinear NSDDE and a system show that the family of two-step Maruyama methods have better stability than previous two-step Maruyama methods.

Suggested Citation

  • Li, Xiuping & Cao, Wanrong, 2015. "On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 373-381.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:373-381
    DOI: 10.1016/j.amc.2015.04.003
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    Cited by:

    1. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    2. Ahmadian, D. & Farkhondeh Rouz, O. & Ballestra, L.V., 2019. "Stability analysis of split-step θ-Milstein method for a class of n-dimensional stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 413-424.
    3. Haoyi Mo & Xueyan Zhao & Feiqi Deng, 2017. "Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 462-470, February.
    4. Zhenyu Wang & Qiang Ma & Xiaohua Ding, 2020. "Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    5. Mo, Haoyi & Deng, Feiqi & Zhang, Chaolong, 2017. "Exponential stability of the split-step θ-method for neutral stochastic delay differential equations with jumps," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 85-95.
    6. Li, Min & Huang, Chengming, 2020. "Projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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