Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Liying Zhang

Jing Wang

Weien Zhou

Landong Liu

Li Zhang