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Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps

Author

Listed:
  • Amr Abosenna

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    Department of Mathematics, Faculty of Engineering at Shoubra, Benha University, Benha 13511, Egypt)

  • Ghada AlNemer

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Boping Tian

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China)

Abstract

This paper addresses a stochastic pantograph model with Lévy leaps where non-jump coefficients exceed linearity. The partially truncated split-step theta method is introduced and applied to the proposed model. The finite time L ϱ ^ ( ϱ ^ ≥ 2 ) convergence rate of the numerical scheme is obtained. Furthermore, the almost sure polynomial stability of the numerical scheme is investigated and numerical examples are presented to endorse the addressed theorems.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2016-:d:1424931
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    References listed on IDEAS

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    4. 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.
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