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 -

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.