Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations
Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2017-0030
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 2 : pp. 547–565
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19