Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients
Year: 2023
Author: Xiaojuan Wu, Siqing Gan
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 59–75
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.161121.090722
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 59–75
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stochastic differential equation non-globally Lipschitz coefficient split-step theta method strong convergence rate.
Author Details
-
An explicit positivity-preserving scheme for the Heston 3/2-model with order-one strong convergence
Wu, Xiaojuan
Gan, Siqing
Communications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108372
https://doi.org/10.1016/j.cnsns.2024.108372 [Citations: 0]