TY - JOUR
T1 - Convergence Analysis of a Splitting Method for Stochastic Differential Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 673
EP - 692
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/832.html
KW - stochastic differential equation, drift-implicit splitting scheme, Brownian motion.
AB - <p style="text-align: justify;">In this paper, we propose a fully drift-implicit splitting
numerical scheme for the stochastic differential equations driven by the
standard $d$-dimensional Brownian motion. We prove that its strong
convergence rate is of the same order as the standard Euler-Maruyama
method. Some numerical experiments are also carried out to demonstrate
this property. This scheme allows us to use the latest information
inside each iteration in the Euler-Maruyama method so that better
approximate solutions could be obtained than the standard approach.</p>