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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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
Hindawi Limited
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/323ca4bd9c8746a49818d0c29e9500ac |
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| Summary: | 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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