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 - <p style="text-align: justify;">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.</p>