TY - JOUR T1 - Analysis of the Closure Approximation for a Class of Stochastic Differential Equations AU - Yunfeng Cai, Tiejun Li, Jiushu Shao & Zhiming Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 299 EP - 330 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.s06 UR - https://global-sci.org/intro/article_detail/nmtma/12348.html KW - AB -

Motivated by the numerical study of spin-boson dynamics in quantum open systems, we present a convergence analysis of the closure approximation for a class of stochastic differential equations. We show that the naive Monte Carlo simulation of the system by direct temporal 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 and applied to the original spin-boson model with similar structure.