STRONG CONVERGENCE OF THE EULER-MARUYAMA METHOD FOR A CLASS OF STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

JOURNAL OF COMPUTATIONAL MATHEMATICS（2022）

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摘要

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 EulerMaruyama method is 21. 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 21. Moreover, the theoretical results are illustrated by some numerical examples.

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关键词

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

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