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Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions

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  • Mengting Deng
  • Guo Jiang
  • Ting Ke
  • Shiping Wen

Abstract

This paper presents a valid numerical method to solve nonlinear stochastic Itô–Volterra integral equations (SIVIEs) driven by fractional Brownian motion (FBM) with Hurst parameter H∈1/2,1. On the basis of FBM and block pulse functions (BPFs), a new stochastic operational matrix is proposed. The nonlinear stochastic integral equation is converted into a nonlinear algebraic equation by this method. Furthermore, error analysis is given by the pathwise approach. Finally, two numerical examples exhibit the validity and accuracy of the approach.

Suggested Citation

  • Mengting Deng & Guo Jiang & Ting Ke & Shiping Wen, 2021. "Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-11, October.
    • Handle: RePEc:hin:jnddns:4934658
    DOI: 10.1155/2021/4934658
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