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Volume 13, Issue 1
Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients

Xiaojuan Wu & Siqing Gan

DOI: 10.4208/eajam.161121.090722

East Asian J. Appl. Math., 13 (2023), pp. 59-75.

Published online: 2023-01

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  • 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.

  • Keywords

Stochastic differential equation, non-globally Lipschitz coefficient, split-step theta method, strong convergence rate.

  • AMS Subject Headings

60H35, 60H15, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.161121.090722}, url = {http://global-sci.org/intro/article_detail/eajam/21302.html} }
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.

Wu , Xiaojuan and Gan , Siqing. (2023). Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients. East Asian Journal on Applied Mathematics. 13 (1). 59-75. doi:10.4208/eajam.161121.090722
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