Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations
Year: 2020
Author: Liying Zhang, Jing Wang, Weien Zhou, Landong Liu, Li Zhang
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 487–501
Abstract
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 illustrating the convergence and the convergence order with respect to the iteration number $k$, which show the efficiency of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1901-m2018-0085
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 3 : pp. 487–501
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Stochastic differential equations Parareal algorithm Convergence Stochastic Taylor expansion Milstein scheme.