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Strong convergence of the Euler-Maruyama method for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay. (English) Zbl 1439.65228

Summary: This paper mainly focuses on the strong convergence of the Euler-Maruyama method for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay. It is well known that the strong approximation of the Itô integral usually leads to 0.5-order approximation for stochastic problems. However, in this paper, we will show that 1-order strong superconvergence can be obtained for nonlinear stochastic convolution Itô-Volterra integral equations with constant delay under some mild conditions on the kernel of the diffusion term. Finally, some numerical experiments are given to illustrate our theoretical results.

MSC:

65R20 Numerical methods for integral equations
60H20 Stochastic integral equations
45D05 Volterra integral equations
45R05 Random integral equations
65C30 Numerical solutions to stochastic differential and integral equations
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