Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients

被引：2

作者：

Wu, Xiaojuan ^{[1
]}

Gan, Siqing ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Hunan, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2023年 / 13卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Stochastic differential equation; non-globally Lipschitz coefficient; split-step theta method; strong convergence rate; STOCHASTIC DIFFERENTIAL-EQUATIONS; EULER-MARUYAMA METHOD; MEAN-SQUARE CONVERGENCE; VARYING COEFFICIENTS; NUMERICAL-METHODS; STABILITY; APPROXIMATIONS; EXPLICIT; SCHEME; TIME;

D O I：

10.4208/eajam.161121.090722

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 theta is an element of [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.

引用

页码：59 / 75

页数：17

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