Convergence analysis of an iterative numerical algorithm for solving nonlinear stochastic Itô-Volterra integral equations with m-dimensional Brownian motion

In this article, a numerical technique based on a combination of the Picard iteration method and hat basis functions to solve nonlinear stochastic Ito-Volterra integral equations with m-dimensional Brownian motion is proposed. The existence and uniqueness theorem for the solution of this class of Ito-Volterra integral equations is proved. Also, convergence analysis of the suggested method is investigated in details. Finally, some numerical examples are provided to demonstrate the accuracy of the proposed method and guarantee the theoretical results.