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Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay

Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Volterra Integral Equations with Time-Dependent Delay
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Year:    2022

Author:    Siyuan Qi, Guangqiang Lan

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 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.]

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2010-m2020-0129

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 437–452

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

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

Author Details

Siyuan Qi

Guangqiang Lan

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