Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations

Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations

Year:    2022

Author:    Wei Zhang

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 607–623

Abstract

In this paper, we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations (SVIEs). It is known that the strong convergence order of the Euler-Maruyama method is $\frac12$. However, the strong superconvergence order $1$ can be obtained for a class of SVIEs if the kernels $\sigma_{i}(t, t) = 0$ for $i=1$ and $2$; otherwise, the strong convergence order is $\frac12$. Moreover, the theoretical results are illustrated by some numerical examples.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2101-m2020-0070

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 4 : pp. 607–623

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Strong convergence Stochastic Volterra integral equations Euler-Maruyama method Lipschitz condition.

Author Details

Wei Zhang