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Strong Convergence of Truncated EM Method for Stochastic Volterra Integral Differential Equations with Hölder Diffusion Coefficients

Author

Listed:
  • Juanting Feng

    (Department of Basic, Yinchuan University of Energy, Yinchuan 750105, China)

  • Qimin Zhang

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

Abstract

The strong convergence of numerical solutions is studied in this paper for stochastic Volterra integral differential equations (SVIDEs) with a Hölder diffusion coefficient using the truncated Euler–Maruyama method. Firstly, the numerical solutions of SVIDEs are obtained based on the Euler–Maruyama method. Then, the p th moment boundedness and strong convergence of truncated the Euler–Maruyama numerical solutions are proven under the local Lipschitz condition and the Khasminskii-type condition. Finally, the convergence rate of the truncated Euler–Maruyama method of the numerical solutions is also discussed under some suitable assumptions.

Suggested Citation

  • Juanting Feng & Qimin Zhang, 2024. "Strong Convergence of Truncated EM Method for Stochastic Volterra Integral Differential Equations with Hölder Diffusion Coefficients," Mathematics, MDPI, vol. 12(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3662-:d:1527276
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