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Volume 38, Issue 3
Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations

Liying Zhang, Jing Wang, Weien Zhou, Landong Liu & Li Zhang

DOI: 10.4208/jcm.1901-m2018-0085

J. Comp. Math., 38 (2020), pp. 487-501.

Published online: 2020-03

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  • 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.

  • Keywords

Stochastic differential equations, Parareal algorithm, Convergence, Stochastic Taylor expansion, Milstein scheme.

  • AMS Subject Headings

60H10, 60H35, 65Y05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lyzhang@lsec.cc.ac.cn (Liying Zhang)

1014944214@qq.com (Jing Wang)

weienzhou@nudt.edu.cn (Weien Zhou)

Liuld@cumtb.edu.cn (Landong Liu)

lytzhangli@buu.edu.cn (Li Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-487, author = {Zhang , LiyingWang , JingZhou , WeienLiu , Landong and Zhang , Li}, title = {Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1901-m2018-0085}, url = {http://global-sci.org/intro/article_detail/jcm/15797.html} }
TY - JOUR T1 - Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations AU - Zhang , Liying AU - Wang , Jing AU - Zhou , Weien AU - Liu , Landong AU - Zhang , Li JO - Journal of Computational Mathematics VL - 3 SP - 487 EP - 501 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1901-m2018-0085 UR - https://global-sci.org/intro/article_detail/jcm/15797.html KW - Stochastic differential equations, Parareal algorithm, Convergence, Stochastic Taylor expansion, Milstein scheme. AB -

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.

Zhang , LiyingWang , JingZhou , WeienLiu , Landong and Zhang , Li. (2020). Convergence Analysis of Parareal Algorithm Based on Milstein Scheme for Stochastic Differential Equations. Journal of Computational Mathematics. 38 (3). 487-501. doi:10.4208/jcm.1901-m2018-0085
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