Volume 12, Issue 2
Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations

Jianfang Gao, Shufang Ma & Hui Liang

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 547-565.

Published online: 2018-12

Preview Purchase PDF 143 6228
Export citation
  • Abstract

This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations (SVIDEs). The solvability and the mean-square boundedness of numerical solutions are presented. In view of the properties of the Itô integral, different from the known stochastic problems, it is proved that the strong convergence order of the semi-implicit Euler method is 1, although the approximation order of the Itô integral is 0.5. The theoretical results are illustrated by extensive numerical examples.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-12-547, author = {}, title = {Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {547--565}, abstract = {

This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations (SVIDEs). The solvability and the mean-square boundedness of numerical solutions are presented. In view of the properties of the Itô integral, different from the known stochastic problems, it is proved that the strong convergence order of the semi-implicit Euler method is 1, although the approximation order of the Itô integral is 0.5. The theoretical results are illustrated by extensive numerical examples.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0030}, url = {http://global-sci.org/intro/article_detail/nmtma/12908.html} }
TY - JOUR T1 - Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 547 EP - 565 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2017-0030 UR - https://global-sci.org/intro/article_detail/nmtma/12908.html KW - AB -

This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations (SVIDEs). The solvability and the mean-square boundedness of numerical solutions are presented. In view of the properties of the Itô integral, different from the known stochastic problems, it is proved that the strong convergence order of the semi-implicit Euler method is 1, although the approximation order of the Itô integral is 0.5. The theoretical results are illustrated by extensive numerical examples.

Jianfang Gao, Shufang Ma & Hui Liang. (2020). Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 547-565. doi:10.4208/nmtma.OA-2017-0030
Copy to clipboard
The citation has been copied to your clipboard