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Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Convolution Itô-Volterra Integral Equations with Constant Delay

Author

Listed:
  • Shu Fang Ma

    (Northeast Forest University)

  • Jian Fang Gao

    (Harbin Normal University)

  • Zhan Wen Yang

    (Harbin Institute of Technology)

Abstract

This paper mainly focuses on the strong convergence of the Euler-Maruyama method for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay. It is well known that the strong approximation of the Itô integral usually leads to 0.5-order approximation for stochastic problems. However, in this paper, we will show that 1-order strong superconvergence can be obtained for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay under some mild conditions on the kernel of the diffusion term. Finally, some numerical experiments are given to illustrate our theoretical results.

Suggested Citation

  • Shu Fang Ma & Jian Fang Gao & Zhan Wen Yang, 2020. "Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Convolution Itô-Volterra Integral Equations with Constant Delay," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 223-235, March.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09702-y
    DOI: 10.1007/s11009-019-09702-y
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