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Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations

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  • Ranjbar, Hassan

Abstract

This study investigates the theoretical analysis and numerical approximation of generalized stochastic Volterra integro-differential equations. First, we examine the existence, uniqueness, boundedness and Hölder continuity of the exact solutions for generalized SVIDEs. To numerically solve, the split-step ϑ integrator is proposed. We then demonstrate the boundedness of the numerical solution. Further, it has been shown that the scheme is strongly convergent with order half. Numerical experiments are carried out to support our findings.

Suggested Citation

  • Ranjbar, Hassan, 2025. "Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 165-186.
    • Handle: RePEc:eee:matcom:v:233:y:2025:i:c:p:165-186
    DOI: 10.1016/j.matcom.2025.01.021
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    References listed on IDEAS

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    1. Peng Hu & Chengming Huang, 2014. "The Stochastic Θ‐Method for Nonlinear Stochastic Volterra Integro‐Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Liu, Yufen & Cao, Wanrong & Li, Yuelin, 2022. "Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. Yang, Huizi & Yang, Zhanwen & Ma, Shufang, 2019. "Theoretical and numerical analysis for Volterra integro-differential equations with Itô integral under polynomially growth conditions," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 70-82.
    4. Peng Hu & Chengming Huang, 2014. "The Stochastic -Method for Nonlinear Stochastic Volterra Integro-Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, October.
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