Motivated by the numerical study of the spin-boson dynamics in quantum open systems, we present a convergence analysis of the moment closure approximation for a class of stochastic differential equations. We show that the naive Monte Carlo simulation of the system by direct tem- poral discretization is not feasible through variance analysis and numerical experiments. We also show that the Wiener chaos expansion exhibits very slow convergence and high computational cost. Though efficient and accurate, the rationale of the moment closure approach remains mysterious. We rigorously prove that the low moments in the moment closure approximation of the considered model are of exponential convergence to the exact result. It is further extended to more general nonlinear problems with similar structure.

李铁军, 北京大学数学科学学院教授, 教育部新世纪人才支持计划及国家自然科学基金委优秀青年基金获得者。研究领域为随机模型、理论及算法, 近年来主要关注于化学反应随机动力学的稀有事件, 发展了化学反应随机系统的两尺度大偏差及生物体系能量景观理论, 在复杂网络模型约化及复杂流体的随机模型分析等方面也取得了一些重要成果。迄今共发表论文四十余篇。