A modified split-step truncated Euler-Maruyama method for SDEs with non-globally Lips- chitz continuous coefficients

被引：1

作者：

Haghighi, Amir ^{[1
]}

机构：

[1] Razi Univ, Fac Sci, Dept Math, Kermanshah, Iran

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2023年 / 11卷 / 03期

关键词：

Local Lipschitz condition; Khasiminskii condition; Truncated method; Split-step method; Strong convergence; STOCHASTIC DIFFERENTIAL-EQUATIONS; STRONG-CONVERGENCE; STABILITY; APPROXIMATION;

D O I：

10.22034/cmde.2022.52638.2212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an explicit diffuse the split-step truncated Euler-Maruyama (DSSTEM) method for stochastic differential equations with non-global Lipschitz coefficients. We investigate the strong convergence of the new method under local Lipschitz and Khasiminskii-type conditions. We show that the newly proposed method achieves a strong convergence rate arbitrarily close to half under some additional conditions. Finally, we illustrate the efficiency and performance of the proposed method with numerical results.

引用

页码：522 / 534

页数：13

共 25 条

[1]

[Anonymous], 2007, Stochastic Differential Equations and Applications, DOI [10.1533/9780857099402, DOI 10.1533/9780857099402]

[2] Stability analysis of high order Runge-Kutta methods for index 1 stochastic differential-algebraic equations with scalar noise [J].

Avaji, M. ;

Akbarfam, A. Jodayree ;

Haghighi, A. .

APPLIED MATHEMATICS AND COMPUTATION, 2019, 362

[3] The truncated Milstein method for stochastic differential equations with commutative noise [J].

Guo, Qian ;

Liu, Wei ;

Mao, Xuerong ;

Yue, Rongxian .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 338 :298-310

[4] The partially truncated Euler-Maruyama method and its stability and boundedness [J].

Guo, Qian ;

Liu, Wei ;

Mao, Xuerong ;

Yue, Rongxian .

APPLIED NUMERICAL MATHEMATICS, 2017, 115 :235-251

[5] Split-step double balanced approximation methods for stiff stochastic differential equations [J].

Haghighi, Amir ;

Rossler, Andreas .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (05) :1030-1047

[6] Strong convergence of Euler-type methods for nonlinear stochastic differential equations [J].

Higham, DJ ;

Mao, XR ;

Stuart, AM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (03) :1041-1063

[7] Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations [J].

Hu, Liangjian ;

Li, Xiaoyue ;

Mao, Xuerong .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 337 :274-289

[8] STRONG CONVERGENCE OF AN EXPLICIT NUMERICAL METHOD FOR SDES WITH NONGLOBALLY LIPSCHITZ CONTINUOUS COEFFICIENTS [J].

Hutzenthaler, Martin ;

Jentzen, Arnulf ;

Kloeden, Peter E. .

ANNALS OF APPLIED PROBABILITY, 2012, 22 (04) :1611-1641

[9] Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients [J].

Hutzenthaler, Martin ;

Jentzen, Arnulf ;

Kloeden, Peter E. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 467 (2130) :1563-1576

[10]

Kloeden P. E., 2007, NUMERICAL SOLUTION S

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