Analysis of the Closure Approximation for a Class of Stochastic Differential Equations. Issue 2 (9th May 2017)

• Record Type: Journal Article
• Authors: Cai, Yunfeng; Li, Tiejun; Shao, Jiushu; Wang, Zhiming
• Is Part Of: Numerical mathematics. Volume 10:Issue 2(2017)
• Page Start: 299
• Page End: 330
• Publication Date: 2017-05-09
• Subjects: 65C30, -- 65F99, -- 82C31; Moment closure, -- spin-boson dynamics, -- convergence analysis, -- banded structure; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.s06
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: 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.