A numerical method for solving \(m\)-dimensional stochastic itô-Volterra integral equations by stochastic operational matrix. (English) Zbl 1238.65007

Summary: 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 \([0,1)\) to solve \(m\)-dimensional stochastic Itô-Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, m-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 \(O(h)\). Furthermore, a 95% confidence interval of the errors’ mean is made, the results shows that the approximate solutions have a credible degree of accuracy.


65C30 Numerical solutions to stochastic differential and integral equations
60H20 Stochastic integral equations
45R05 Random integral equations
65R20 Numerical methods for integral equations
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