A Haar wavelet method for linear and nonlinear stochastic Itô–Volterra integral equation driven by a fractional Brownian motion. Issue 5 (3rd September 2021) - Wen, Xiaoxia; Huang, Jin
Abstract: In this paper, a Haar wavelet method is proposed for solving linear and nonlinear stochastic Itô–Volterra integral equation (SIVIE) driven by fractional Brownian motion (FBM) with Hurst parameter H ∈ ( 1 2, 1 ) . This approach reduces the solution of the problem under study to the solution of a linear and nonlinear system of algebraic equations, which is based on the operational matrix and stochastic operational matrix of the Haar wavelets basis (HWB). Moreover, the error estimate and convergence analysis of the method are established in detail. Several numerical examples are presented to test the applicability and efficiency of the proposed method.