TY - JOUR T1 - Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients AU - Wu , Xiaojuan AU - Gan , Siqing JO - East Asian Journal on Applied Mathematics VL - 1 SP - 59 EP - 75 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.161121.090722 UR - https://global-sci.org/intro/article_detail/eajam/21302.html KW - Stochastic differential equation, non-globally Lipschitz coefficient, split-step theta method, strong convergence rate. AB -

The present work analyzes the mean-square approximation error of split-step theta methods in a non-globally Lipschitz regime. We show that under a coupled monotonicity condition and polynomial growth conditions, the considered methods with the parameters $θ ∈ [1/2, 1]$ have convergence rate of order $1/2.$ This covers a class of stochastic differential equations with super-linearly growing diffusion coefficients such as the popular $3/2$-model in finance. Numerical examples support the theoretical results.