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Volume 40, Issue 3
Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay

Siyuan Qi & Guangqiang Lan

DOI: 10.4208/jcm.2010-m2020-0129

J. Comp. Math., 40 (2022), pp. 437-452.

Published online: 2022-02

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  • Abstract

We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper. Strong convergence rate (at fixed point) of the corresponding Euler-Maruyama method is obtained when coefficients $f$ and $g$ both satisfy local Lipschitz and linear growth conditions. An example is provided to interpret our conclusions. Our result generalizes and improves the conclusion in [J. Gao, H. Liang, S. Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348 (2019) 385-398.]

  • Keywords

Stochastic Volterra integral equation, Euler-Maruyama method, Strong convergence, Time-dependent delay.

  • AMS Subject Headings

65C30, 65C20, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-40-437, author = {Qi , Siyuan and Lan , Guangqiang}, title = {Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {3}, pages = {437--452}, abstract = {

We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper. Strong convergence rate (at fixed point) of the corresponding Euler-Maruyama method is obtained when coefficients $f$ and $g$ both satisfy local Lipschitz and linear growth conditions. An example is provided to interpret our conclusions. Our result generalizes and improves the conclusion in [J. Gao, H. Liang, S. Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348 (2019) 385-398.]

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2010-m2020-0129}, url = {http://global-sci.org/intro/article_detail/jcm/20245.html} }
TY - JOUR T1 - Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay AU - Qi , Siyuan AU - Lan , Guangqiang JO - Journal of Computational Mathematics VL - 3 SP - 437 EP - 452 PY - 2022 DA - 2022/02 SN - 40 DO - http://doi.org/10.4208/jcm.2010-m2020-0129 UR - https://global-sci.org/intro/article_detail/jcm/20245.html KW - Stochastic Volterra integral equation, Euler-Maruyama method, Strong convergence, Time-dependent delay. AB -

We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper. Strong convergence rate (at fixed point) of the corresponding Euler-Maruyama method is obtained when coefficients $f$ and $g$ both satisfy local Lipschitz and linear growth conditions. An example is provided to interpret our conclusions. Our result generalizes and improves the conclusion in [J. Gao, H. Liang, S. Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348 (2019) 385-398.]

Siyuan Qi & Guangqiang Lan. (2022). Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay. Journal of Computational Mathematics. 40 (3). 437-452. doi:10.4208/jcm.2010-m2020-0129
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