A new numerical algorithm based on least squares method for solving stochastic Itô-Volterra integral equations

In conjunction with least squares method and generalized hat functions, we propose a new algorithm for stochastic Itô-Volterra integral equations. Firstly, the original problem is turned into solving a linear system of equations. Further, an efficient strategy is constructed to figure out the relevant coefficients of the linear system of equations. For computation purposes, throughout this paper, stochastic Itô integrals are transformed into conventional integrals using integration by parts formula. We also theoretically examine the convergence of the proposed approach. In the end, we provide two related examples to verify the reliability and accuracy of our proposed method. And in comparison with their numerical errors of the traditional block pulse method, the error of our presented approach is smaller.