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

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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.

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Acknowledgments

This work is supported by the Fundamental Research Funds for Central Universities (2572018BC19).

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Authors and Affiliations

  1. Department of Mathematics, Northeast Forest University, Harbin, Heilongjiang, China

    Shu Fang Ma

  2. School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, China

    Jian Fang Gao

  3. Department of Mathematic, Harbin Institute of Technology, Harbin, Heilongjiang, China

    Zhan Wen Yang

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  1. Shu Fang Ma
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  2. Jian Fang Gao
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  3. Zhan Wen Yang
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Correspondence to Jian Fang Gao.

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Ma, S.F., Gao, J.F. & Yang, Z.W. Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Convolution Itô-Volterra Integral Equations with Constant Delay. Methodol Comput Appl Probab 22, 223–235 (2020). https://doi.org/10.1007/s11009-019-09702-y

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  • DOI: https://doi.org/10.1007/s11009-019-09702-y

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