Numerical Solution Based on Hat Functions for Solving Nonlinear Stochastic Itô Volterra Integral Equations Driven by Fractional Brownian Motion

2016 ◽  
Vol 14 (1) ◽  
Author(s):  
B. Hashemi ◽  
M. Khodabin ◽  
K. Maleknejad
Keyword(s):  
Brownian Motion ◽  
Numerical Solution ◽  
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.

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