Galerkin Approximation for Stochastic Volterra Integral Equations with Doubly Singular Kernels
Abstract
:1. Introduction
2. Preliminaries
2.1. Lemmas and Assumption
2.2. A Numerical Approximation of White Noise for Stochastic Integral
2.3. The Discontinuous Galerkin Method
3. Main Result
4. Numerical Simulation
- Case I:
- Case II:
- Case III:
- Case IV:
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Convergence Rate | ||||
---|---|---|---|---|
0.4 | 0.2 | 0.1 | 0.1 | 0.3 |
0.4 | 0.2 | 0.2 | 0.1 | 0.2 |
0.4 | 0.4 | 0.1 | 0.1 | 0.2 |
0.4 | 0.2 | 0.1 | 0.2 | 0.2 |
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Li, Y.; Song, W.; Jiang, Y.; Kudreyko, A. Galerkin Approximation for Stochastic Volterra Integral Equations with Doubly Singular Kernels. Fractal Fract. 2022, 6, 311. https://doi.org/10.3390/fractalfract6060311
Li Y, Song W, Jiang Y, Kudreyko A. Galerkin Approximation for Stochastic Volterra Integral Equations with Doubly Singular Kernels. Fractal and Fractional. 2022; 6(6):311. https://doi.org/10.3390/fractalfract6060311
Chicago/Turabian StyleLi, Yuyuan, Wanqing Song, Yanan Jiang, and Aleksey Kudreyko. 2022. "Galerkin Approximation for Stochastic Volterra Integral Equations with Doubly Singular Kernels" Fractal and Fractional 6, no. 6: 311. https://doi.org/10.3390/fractalfract6060311