An adaptive Euler-Maruyama scheme for SDDEs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914851826171904 |
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| author | Liu, Dongyang Song, Minghui Zhang, Yuhang |
| author_facet | Liu, Dongyang Song, Minghui Zhang, Yuhang |
| contents | This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step size based on the growth of the drift term. Differing slightly from the conventional Euler-Maruyama format, this paper addresses the estimation of the delay term by substituting it with the numerically obtained solution closest to the left endpoint.This approach overcomes the challenge of numerical nodes not falling within the nodes after subtracting the delay. The paper proves the convergence of the numerical method for a class of non-global Lipschitz continuous SDDEs under the assumption that the step size function satisfies certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An adaptive Euler-Maruyama scheme for SDDEs Liu, Dongyang Song, Minghui Zhang, Yuhang Numerical Analysis This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step size based on the growth of the drift term. Differing slightly from the conventional Euler-Maruyama format, this paper addresses the estimation of the delay term by substituting it with the numerically obtained solution closest to the left endpoint.This approach overcomes the challenge of numerical nodes not falling within the nodes after subtracting the delay. The paper proves the convergence of the numerical method for a class of non-global Lipschitz continuous SDDEs under the assumption that the step size function satisfies certain conditions. |
| title | An adaptive Euler-Maruyama scheme for SDDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.10244 |