A numerical method for solving mm-dimensional stochastic Itô–Volterra integral equations by stochastic operational matrix

The multidimensional Itô–Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval [0,1)[0,1) to solve m-dimensional stochastic Itô–Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, mm-dimensional stochastic Itô–Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is O(h)O(h). Furthermore, a 95% confidence interval of the errors’ mean is made, the results shows that the approximate solutions have a credible degree of accuracy.