A Haar wavelet method for linear and nonlinear stochastic Itô–Volterra integral equation driven by a fractional Brownian motion. Issue 5 (3rd September 2021)

• Record Type: Journal Article
• Authors: Wen, Xiaoxia; Huang, Jin
• Is Part Of: Stochastic analysis and applications. Volume 39:Issue 5(2021)
• Page Start: 926
• Page End: 943
• Publication Date: 2021-09-03
• Subjects: Fractional Brownian motion -- Haar wavelets basis -- stochastic Itô–Volterra integral equation -- stochastic operational matrix -- convergence analysis -- error estimation; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1858873
• Languages: English
• ISSNs: 0736-2994

Abstract

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.