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 exac...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.展开更多
基金We are very grateful to the reviewers for reading our paper carefully and providing many useful comments and suggestions.The first author is supported by NNSFC(Nos.11601514,11771444,11801556 and 11971458)The fourth author is supported by Beijing Nature Science Foundation(No.1152002)This work is also supported by NSF of Jiangsu Province of China(BK.20130779).
文摘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.
