CONVERGENCE ANALYSIS OF PARAREAL ALGORITHM BASED ON MILSTEIN SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Stochastic differential equations Parareal algorithm Convergence Stochastic Taylor expansion Milstein scheme
• 年，卷（期）: 2020,（3）
• 页码范围: 487-501
• 页数: 15页
• 语种: 英文
• DOI: 10.4208/jcm.1901-m2018-0085

摘要

In this paper,we propose a parareal algorithm for stochastic differential equations (SDEs),which proceeds as a two-level temporal parallelizable integrator with the Milstein scheme as the coarse propagator and the exact solution as the fine propagator.The convergence order of the proposed algorithm is analyzed under some regular assumptions.Finally,numerical experiments are dedicated to illustrate the convergence and the convergence order with respect to the iteration number k,which show the efficiency of the proposed method.