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

共 39 条

[1] Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
Andersson, Adam
Kruse, Raphael
[J]. BIT NUMERICAL MATHEMATICS, 2017, 57 (01) : 21 - 53
[2] Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients
不详
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 236 (1112) : 1 - +
[3] Stochastic C-Stability and B-Consistency of Explicit and Implicit Milstein-Type Schemes
Beyn, Wolf-Juergen
Isaak, Elena
Kruse, Raphael
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2017, 70 (03) : 1042 - 1077
[4] Stochastic C-Stability and B-Consistency of Explicit and Implicit Euler-Type Schemes
Beyn, Wolf-Juergen
Isaak, Elena
Kruse, Raphael
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2016, 67 (03) : 955 - 987
[5] An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients
Chassagneux, Jean-Francois
Jacquier, Antoine
Mihaylov, Ivo
[J]. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 2016, 7 (01): : 993 - 1021
[6] ADAPTIVE EULER-MARUYAMA METHOD FOR SDES WITH NONGLOBALLY LIPSCHITZ DRIFT
Fang, Wei
Giles, Michael B.
[J]. ANNALS OF APPLIED PROBABILITY, 2020, 30 (02) : 526 - 560
[7] Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients
Gan, Siqing
He, Youzi
Wang, Xiaojie
[J]. APPLIED NUMERICAL MATHEMATICS, 2020, 152 : 379 - 402
[8] The truncated Milstein method for stochastic differential equations with commutative noise
Guo, Qian
Liu, Wei
Mao, Xuerong
Yue, Rongxian
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 338 : 298 - 310
[9] Heston S., 1997, Technical report
[10] Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations
Higham, Desmond J.
Mao, Xuerong
Yuan, Chenggui
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) : 592 - 609

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