In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

中文翻译：

---

基于最小二乘法和块脉冲函数的多维随机Itô-Volterra积分方程数值解

本文提出了一种基于最小二乘法和块脉冲函数的方法来求解多维随机Itô-Volterra积分方程。将Itô-Volterra积分方程转换为线性代数方程。此外，误差分析由等轴测特性和Doob不等式给出。数值算例验证了该方法的有效性和准确性。