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

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 nonl...

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Autores principales:	Mengting Deng, Guo Jiang, Ting Ke
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/323ca4bd9c8746a49818d0c29e9500ac
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spelling	oai:doaj.org-article:323ca4bd9c8746a49818d0c29e9500ac2021-11-08T02:35:25ZNumerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions1607-887X10.1155/2021/4934658https://doaj.org/article/323ca4bd9c8746a49818d0c29e9500ac2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/4934658https://doaj.org/toc/1607-887XThis 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.Mengting DengGuo JiangTing KeHindawi LimitedarticleMathematicsQA1-939ENDiscrete Dynamics in Nature and Society, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Mengting Deng Guo Jiang Ting Ke Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
description	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.
format	article
author	Mengting Deng Guo Jiang Ting Ke
author_facet	Mengting Deng Guo Jiang Ting Ke
author_sort	Mengting Deng
title	Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
title_short	Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
title_full	Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
title_fullStr	Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
title_full_unstemmed	Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
title_sort	numerical solution of nonlinear stochastic itô–volterra integral equations driven by fractional brownian motion using block pulse functions
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/323ca4bd9c8746a49818d0c29e9500ac
work_keys_str_mv	AT mengtingdeng numericalsolutionofnonlinearstochasticitovolterraintegralequationsdrivenbyfractionalbrownianmotionusingblockpulsefunctions AT guojiang numericalsolutionofnonlinearstochasticitovolterraintegralequationsdrivenbyfractionalbrownianmotionusingblockpulsefunctions AT tingke numericalsolutionofnonlinearstochasticitovolterraintegralequationsdrivenbyfractionalbrownianmotionusingblockpulsefunctions
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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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