Strong Convergence of the Euler-Maruyama Method for Nonlinear Stochastic Convolution Itô-Volterra Integral Equations with Constant Delay

Shu Fang Ma (), Jian Fang Gao () and Zhan Wen Yang ()
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Shu Fang Ma: Northeast Forest University
Jian Fang Gao: Harbin Normal University
Zhan Wen Yang: Harbin Institute of Technology

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 1, 223-235

Abstract: Abstract 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.

Keywords: Stochastic Itô-Volterra integral equations; Constant delay; Euler-maruyama method; Strong superconvergence order; 65C20; 65C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09702-y

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