An iterative technique for the numerical solution of nonlinear stochastic Itô -Volterra integral equations

The main aim of this study is to propose a numerical iterative approach for obtaining approximate solutions of nonlinear stochastic Itô -Volterra integral equations. The method is based on a combination of the successive approximations method, the linear spline interpolation and Itô approximation. Moreover, the convergence analysis of this method is investigated in detail. To confirm the validity and applicability of the new method, several illustrative examples and some applications are presented.