发表机构
School of Mathematics and Statistics, Yunnan University; School of Statistics and Data Science, Jiangxi University of Finance and Economics（云南大学数学与统计学院; 江西财经大学统计与数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对指标1随机微分代数方程，提出结构保持的随机theta Milstein方法，在非全局Lipschitz条件下证明其强一阶收敛并保持代数约束，数值实验验证了理论结果。
AI 中文摘要
本文研究了一类具有时变奇异矩阵和非全局Lipschitz系数的指标1随机微分代数方程(SDAEs)的结构保持随机theta Milstein方法的强收敛阶。奇异矩阵允许随时间变化，同时保持固定的微分代数分解，漂移和扩散系数可能表现出超线性增长。通过利用精确解的指标1代数-微分分解，我们直接在原始SDAE变量中识别约化随机微分方程的Milstein系数，并建立了所提方法在θ∈[1/2,1]时的适定性和约束保持性质。在耦合单调性条件和适当的多项式正则性假设下，证明了该方法在所有时间层上保持代数约束，并在均方根范数下以强一阶收敛。数值实验证实了结构保持性质和理论收敛阶。
英文摘要
This paper studies the strong convergence order of structure-preserving stochastic theta Milstein methods for a class of index-$1$ stochastic differential algebraic equations (SDAEs) with time-dependent singular matrices and non-globally Lipschitz coefficients. The singular matrix is allowed to vary in time while preserving a fixed differential algebraic splitting, and the drift and diffusion coefficients may exhibit superlinear growth. By exploiting the index-$1$ algebraic-differential decomposition of the exact solution, we identify the Milstein coefficient of the reduced stochastic differential equation directly in the original SDAE variables and establish the well-posedness and constraint preserving property of the proposed method for $θ\in[1/2,1]$. Under a coupled monotonicity condition and suitable polynomial regularity assumptions, the method is proved to preserve the algebraic constraints at all time levels and to converge with strong order one in the root mean square norm. Numerical experiments confirm the structure-preserving property and the theoretical convergence order.
