The partially truncated Euler-Maruyama method and its stability and boundedness

被引：53

作者：

Guo, Qian ^{[1
]}

Liu, Wei ^{[1
]}

Mao, Xuerong ^{[2
]}

Yue, Rongxian ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

来源：

APPLIED NUMERICAL MATHEMATICS | 2017年 / 115卷

基金：

上海市自然科学基金; 英国工程与自然科学研究理事会;

关键词：

Stochastic differential equation; Local Lipschitz condition; Khasminskii-type condition; Partially truncated Euler-Maruyama method; Stability; STOCHASTIC DIFFERENTIAL-EQUATIONS; EXPONENTIAL STABILITY; NUMERICAL-SIMULATION; SURE; APPROXIMATION; COEFFICIENTS; SDES;

D O I：

10.1016/j.apnum.2017.01.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The partially truncated Euler-Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong IT-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：235 / 251

页数：17

共 27 条

[1]

Andersson A., ARXIV150900609

[2] Numerical approximation of irregular SDEs via Skorokhod embeddings [J].

Ankirchner, Stefan ;

Kruse, Thomas ;

Urusov, Mikhail .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 440 (02) :692-715

[3]

[Anonymous], 2007, STOCHASTIC DIFFERENT

[4]

Bahar A., 2004, Int. J. Pure Appl. Math., V11, P377

[5] Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations [J].

Berkolaiko, Gregory ;

Buckwar, Evelyn ;

Kelly, Conall ;

Rodkina, Alexandra .

LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2012, 15 :71-83

[6]

Ginzburg V. L., 2009, ZH EKSP TEOR FIZ, P113, DOI DOI 10.1007/978-3-540-68008-6_4

[7] A note on Euler's approximations [J].

Gyongy, I .

POTENTIAL ANALYSIS, 1998, 8 (03) :205-216

[8]

Higham D.J., 2003, LMS J. Comput. Math., V6, P297, DOI DOI 10.1112/S1461157000000462

[9] Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations [J].

Higham, Desmond J. ;

Mao, Xuerong ;

Yuan, Chenggui .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) :592-609

[10]

Hutzenthaler M., ARXIV14010295

← 1 2 3 →