This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. The considered systems are described by second-order stochastic differential-algebraic equations involving an implicitly given Lagrange multiplier process. The explicit representation of the Lagrange multiplier leads to an underlying stochastic ordinary differential equation, the drift coefficient of which is typically not globally one-sided Lipschitz continuous. We investigate a half-explicit, drift-truncated Euler scheme that fulfills the constraint exactly. Pathwise uniform |$L_p$|-convergence is established. The proof is based on a suitable decomposition of the discrete Lagrange multipliers and on norm estimates for the single components, enabling the verification of consistency, semistability and moment growth properties of the scheme.

中文翻译：

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约束随机机械系统的半显式Euler格式的强收敛性

本文涉及具有非线性完整约束的随机机械系统的数值逼近。所考虑的系统由包含隐式给出的拉格朗日乘数过程的二阶随机微分-代数方程式描述。拉格朗日乘数的显式表示导致一个潜在的随机常微分方程，其漂移系数通常不是全局单侧Lipschitz连续的。我们研究了一个精确地满足约束的半显式，漂移截断的Euler方案。路径统一| $ L_p $ |-建立收敛。该证明基于离散拉格朗日乘数的适当分解以及单个分量的范数估计，从而能够验证该方案的一致性，半稳定性和矩增长特性。