Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19364220171201Wilson wavelets for solving nonlinear stochastic integral equations33482938810.22072/wala.2017.59458.1106ENBibi Khadijeh MousaviDepartment of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of KermanAtaollah Askari HemmatDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of KermanMohammad Hossien HeydariShiraz University of Technology, Shiraz,Journal Article20170302A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It\^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It\^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration, the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the efficiency and accuracy of the proposed method.https://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf