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Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability

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  • Liu, Linna
  • Mo, Haoyi
  • Deng, Feiqi

Abstract

In this paper, we propose the split-step theta method for stochastic delay integro-differential equations by the Lagrange interpolation technique and investigate the mean square exponential stability of the proposed scheme. It is shown that the split-step theta method can inherit the mean square exponential stability of the continuous model under the linear growth condition and the proposed stability condition by the delayed differential and difference inequalities established in the paper. A numerical example is given at the end of the paper to illustrate the method and conclusion of the paper. In addition, the convergence of the split-step theta method is proved in the Appendix.

Suggested Citation

  • Liu, Linna & Mo, Haoyi & Deng, Feiqi, 2019. "Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 320-328.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:320-328
    DOI: 10.1016/j.amc.2019.01.073
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    References listed on IDEAS

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    1. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
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    Cited by:

    1. Yu Zhang & Enying Zhang & Longsuo Li, 2022. "The Improved Stability Analysis of Numerical Method for Stochastic Delay Differential Equations," Mathematics, MDPI, vol. 10(18), pages 1-7, September.
    2. Song, Minghui & Geng, Yidan & Liu, Mingzhu, 2021. "Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    3. Li, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    4. Amr Abosenna & Ghada AlNemer & Boping Tian, 2024. "Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps," Mathematics, MDPI, vol. 12(13), pages 1-16, June.

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