TY - JOUR
T1 - Modifying the Split-Step $θ$-Method with Harmonic-Mean Term for Stochastic Differential Equations
AU - Nouri , Kazem
AU - Ranjbar , Hassan
AU - Carlos Cortés López , Juan
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 662
EP - 678
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17874.html
KW - Itô stochastic differential system, split-step method, ODE solver, harmonic-mean,
strong convergence, mean-square stability.
AB - <p style="text-align: justify;">In this paper, we design a class of general split-step methods for solving Itô stochastic differential systems, in which the drift or deterministic increment function can be taken
from special ordinary differential equations solver, based on the harmonic-mean. This method is
justified to have a strong convergence order of $\frac{1}{2}$. Further, we investigate mean-square stability
of the proposed method for linear scalar stochastic differential equation. Finally, some examples
are included to demonstrate the validity and efficiency of the introduced scheme.<br/></p>