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Split-step collocation methods for stochastic Volterra integral equations. (English) Zbl 06873405

Summary: In this paper, a split-step collocation method is proposed for solving linear stochastic Volterra integral equations (SVIEs) with smooth kernels. The Hölder condition and the conditional expectations of the exact solutions are investigated. The solvability and mean-square boundedness of numerical solutions are proved and the strong convergence orders of collocation solutions and iterated collocation solutions are also shown. In addition, numerical experiments are provided to verify the conclusions.

MSC:

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

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