Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912781431734272 |
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| author | Li, Guozhen Li, Xiaoyue Mao, Xuerong |
| author_facet | Li, Guozhen Li, Xiaoyue Mao, Xuerong |
| contents | This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite historical storage. Leveraging approximation theory, we prove the boundedness of the numerical solution's $p$th moment and establish its convergence, achieving a rate of $1/2$ order under polynomially growing coefficients. Furthermore, we refine the scheme to better capture the underlying exponential stability of the exact solution, in both moment and almost sure senses. Finally, numerical experiments are presented to validate our theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay Li, Guozhen Li, Xiaoyue Mao, Xuerong Numerical Analysis This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite historical storage. Leveraging approximation theory, we prove the boundedness of the numerical solution's $p$th moment and establish its convergence, achieving a rate of $1/2$ order under polynomially growing coefficients. Furthermore, we refine the scheme to better capture the underlying exponential stability of the exact solution, in both moment and almost sure senses. Finally, numerical experiments are presented to validate our theoretical results. |
| title | Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.00475 |