时滞后向EM法下混合中立型随机时滞微分方程的数值解
The Backward Euler-Maruyama Methodwith Time Delay for the NumericalSolutions of Hybrid Neutral StochasticDifferential Delay Equations
DOI: 10.12677/PM.2026.163078, PDF,   
作者: 林秀琴：广州软件学院基础与通识教育中心，广东 广州
关键词: 后向 EM 法；中立型随机时滞微分方程；数值解；Backward Euler-Maruyama Method； NSDDEs； Numerical Solutions
摘要: 本文主要研究中立型随机时滞微分方程数值解的近似问题。据目前已有成果来看，有关后向 EM 法，在滞后因子控制领域内的研究还存在空缺。因此，本文基于一类带时滞控制的向后 EM 法， 对中立型随机时滞微分方程数值解的近似问题展开研究，并基于系统的指数稳定性，验证了本文 所给控制系统中近似解的存在性及合理性。
Abstract: This paper mainly focuses on the approximation problem of numerical solutions for neutral stochastic delay differential equations (NSDDEs). Based on current research results, there is still a gap in the study of the backward Euler-Maruyama (BEM) method in the field of delay factor control. Therefore, based on the BEM method with delay control systems, this paper investigates the approximation problem of numerical solutions for neutral stochastic delay differential equations, and verifies the existence and rationality of the approximate solutions in the control system considered in this paper.
文章引用：林秀琴. 时滞后向EM法下混合中立型随机时滞微分方程的数值解[J]. 理论数学, 2026, 16(3): 146-154. https://doi.org/10.12677/PM.2026.163078

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