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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 |

### Keywords:

stochastic Volterra integral equations; split-step collocation methods; split-step backward Euler method; strong convergence order
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\textit{Y. Xiao} et al., J. Integral Equations Appl. 30, No. 1, 197--218 (2018; Zbl 06873405)

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