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<p>This paper is concerned with the strong convergence of the projected Euler-Maruyama (PEM) method for neutral stochastic delay differential equations (NSDDEs) with variable delays. First, the notions of C-stability and B-consistency are defined for NSDDEs. Subsequently, under a global monotone condition, a fundamental theorem on strong convergence is established for general one-step methods applied to nonlinear NSDDEs. We then construct the PEM method, an explicit one-step scheme, and prove its C-stability, B-consistency, and strong convergence of order 1/2. Finally, a numerical experiment is presented to validate the results.</p>

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Strong Convergence Order of the Projected Euler-Maruyama Method for Neutral Stochastic Delay Differential Equations Under a Global Monotone Condition

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • Chao Yue

摘要

This paper is concerned with the strong convergence of the projected Euler-Maruyama (PEM) method for neutral stochastic delay differential equations (NSDDEs) with variable delays. First, the notions of C-stability and B-consistency are defined for NSDDEs. Subsequently, under a global monotone condition, a fundamental theorem on strong convergence is established for general one-step methods applied to nonlinear NSDDEs. We then construct the PEM method, an explicit one-step scheme, and prove its C-stability, B-consistency, and strong convergence of order 1/2. Finally, a numerical experiment is presented to validate the results.