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Volume 40, Issue 4
Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations

Wei Zhang

DOI: 10.4208/jcm.2101-m2020-0070

J. Comp. Math., 40 (2022), pp. 607-623.

Published online: 2022-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65L20, 65C40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

weizhanghlj@163.com (Wei Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-607, author = {Zhang , Wei}, title = {Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2020-0070}, url = {http://global-sci.org/intro/article_detail/jcm/20503.html} }
TY - JOUR T1 - Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations AU - Zhang , Wei JO - Journal of Computational Mathematics VL - 4 SP - 607 EP - 623 PY - 2022 DA - 2022/04 SN - 40 DO - http://doi.org/10.4208/jcm.2101-m2020-0070 UR - https://global-sci.org/intro/article_detail/jcm/20503.html KW - Strong convergence, Stochastic Volterra integral equations, Euler-Maruyama method, Lipschitz condition. AB -

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.

Zhang , Wei. (2022). Strong Convergence of the Euler-Maruyama Method for a Class of Stochastic Volterra Integral Equations. Journal of Computational Mathematics. 40 (4). 607-623. doi:10.4208/jcm.2101-m2020-0070
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