In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the sample average approximate method and time-stepping method are adopted to get the numerical solutions. Furthermore, a regularization approximation is introduced to the second case to ensure the uniqueness of solutions. The corresponding convergence analysis is conducted, and numerical examples are presented to illustrate the convergence results we derived. Finally, we provide numerical results which come from applications involving dynamic traffic flow problems to support our theorems.

本文研究了一类由一个常微分方程和一个随机互补问题组成的微分线性随机互补系统。在线性随机互补问题的系数矩阵的两种情况下，获得了该系统解的存在性：P矩阵和正半定矩阵。对于第一种情况，采用样本平均近似法和时间步长法进行数值求解。此外，将正则化近似引入第二种情况以确保解的唯一性。进行了相应的收敛性分析，并通过数值例子说明了我们得出的收敛结果。最后，