scholarly journals Numerical method for solving linear stochasticIto--Volterra integral equations driven by fractional Brownian motion using hat functions

2017 ◽  
Vol 41 ◽  
pp. 611-624 ◽  
Author(s):  
Bentol Hoda HASHEMI ◽  
Morteza KHODABIN ◽  
Khosrow MALEKNEJAD
Keyword(s):  
Brownian Motion ◽  
Numerical Method ◽  
Fractional Brownian Motion ◽  
Integral Equations ◽  
Volterra Integral Equations

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

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mengting Deng ◽  
Guo Jiang ◽  
Ting Ke
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Integral Equations ◽  
Stochastic Integral ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Hurst Parameter ◽  
Stochastic Integral Equation ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix

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.

Numerical solution of nonlinear stochastic Itô – Volterra integral equation driven by fractional Brownian motion

2020 ◽  
Vol 37 (9) ◽  
pp. 3243-3268
Author(s):  
S. Saha Ray ◽  
S. Singh
Keyword(s):  
Integral Equation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Stochastic Integral ◽  
Bernstein Polynomials ◽  
Numerical Results ◽  
Content Type ◽  
Stochastic Integral Equations

Purpose This paper aims to study fractional Brownian motion and its applications to nonlinear stochastic integral equations. Bernstein polynomials have been applied to obtain the numerical results of the nonlinear fractional stochastic integral equations. Design/methodology/approach Bernstein polynomials have been used to obtain the numerical solutions of nonlinear fractional stochastic integral equations. The fractional stochastic operational matrix based on Bernstein polynomial has been used to discretize the nonlinear fractional stochastic integral equation. Convergence and error analysis of the proposed method have been discussed. Findings Two illustrated examples have been presented to justify the efficiency and applicability of the proposed method. The corresponding obtained numerical results have been compared with the exact solutions to establish the accuracy and efficiency of the proposed method. Originality/value To the best of the authors’ knowledge, nonlinear stochastic Itô–Volterra integral equation driven by fractional Brownian motion has been for the first time solved by using Bernstein polynomials. The obtained numerical results well establish the accuracy and efficiency of the proposed method.

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