Title: Strong convergence rates of stochastic theta methods for index 1 stochastic differential algebraic equations under non-globally Lipschitz conditions Show Chinese title

Title: 随机θ方法在非全局Lipschitz条件下对索引1随机微分代数方程的强收敛率

Abstract: This work investigates numerical approximations of index 1 stochastic differential algebraic equations (SDAEs) with non-constant singular matrices under non-global Lipschitz conditions. Analyzing the strong convergence rates of numerical solutions in this setting is highly nontrivial, due to both the singularity of the constraint matrix and the superlinear growth of the coefficients. To address these challenges, we develop an approach for establishing mean square convergence rates of numerical methods for SDAEs under global monotonicity conditions. Specifically, we prove that each stochastic theta method with $\theta \in [\frac{1}{2},1]$ achieves a mean square convergence rate of order $\frac{1}{2}$. Theoretical findings are further validated through a series of numerical experiments. Show Chinese abstract

Abstract: 这项工作研究了在非全局利普希茨条件下，具有非常数奇异矩阵的索引1随机微分代数方程（SDAEs）的数值逼近。 在这种情况下分析数值解的强收敛率是非常困难的，这是由于约束矩阵的奇异性以及系数的超线性增长。 为了解决这些挑战，我们开发了一种方法，在全局单调性条件下建立SDAEs数值方法的均方收敛率。 具体而言，我们证明了每个带有$\theta \in [\frac{1}{2},1]$的随机θ方法可达到阶数为$\frac{1}{2}$的均方收敛率。 理论结果通过一系列数值实验进一步验证。