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.
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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.