TY - JOUR
T1 - Split-Step Forward Milstein Method for Stochastic Differential Equation
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 970
EP - 981
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/668.html
KW - Stochastic differential equation, Explicit method, Mean convergence, Mean square convergence, Stability, Numerical experiment.
AB - <p style="text-align: justify;">In this paper, we consider the problem of computing numerical
solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit
method, the split-step forward Milstein (SSFM) method, is constructed
for solving SDEs. It is proved that the SSFM method is convergent with strong
order $\gamma=1$ in the mean-square sense. The analysis of stability shows that the
mean-square stability properties of the method proposed in this paper are an
improvement on the mean-square stability properties of the Milstein method
and three stage Milstein methods.</p>