@Article{EAJAM-13-59,
author = {Wu , Xiaojuan and Gan , Siqing},
title = {Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {1},
pages = {59--75},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.161121.090722},
url = {http://global-sci.org/intro/article_detail/eajam/21302.html}
}