CONVERGENCE OF THE EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G- BROWNIAN MOTION

被引：1

作者：

Liu, Cunxia ^{[1
]}

Lu, Wen ^{[1
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 61卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Euler-Maruyama method; convergence rate; stochastic differen- tial equation; G-expectation; G-Brownian motion; REPRESENTATION THEOREM; CALCULUS; STABILITY; SCHEME; SDES;

D O I：

10.4134/BKMS.b230354

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with the Euler-Maruyama (EM) scheme for stochastic differential equations driven by G-Brownian motion (G-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for G-SDEs are established.

引用

页码：917 / 932

页数：16

共 27 条

[1]

[Anonymous], 1999, Applications of Mathematics

[2] On the Existence and Uniqueness of Solutions to Stochastic Differential Equations Driven by G-Brownian Motion with Integral-Lipschitz Coefficients [J].

Bai, Xue-peng ;

Lin, Yi-qing .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2014, 30 (03) :589-610

[3] Approximations of McKean-Vlasov Stochastic Differential Equations with Irregular Coefficients [J].

Bao, Jianhai ;

Huang, Xing .

JOURNAL OF THEORETICAL PROBABILITY, 2022, 35 (02) :1187-1215

[4] Convergence Rate of Euler-Maruyama Scheme for SDEs with Holder-Dini Continuous Drifts [J].

Bao, Jianhai ;

Huang, Xing ;

Yuan, Chenggui .

JOURNAL OF THEORETICAL PROBABILITY, 2019, 32 (02) :848-871

[5] CONVERGENCE RATE OF EM SCHEME FOR SDDEs [J].

Bao, Jianhai ;

Yuan, Chenggui .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (09) :3231-3243

[6] Stability equivalence between the stochastic differential delay equations driven by G-Brownian motion and the Euler-Maruyama method [J].

Deng, Shounian ;

Fei, Chen ;

Fei, Weiyin ;

Mao, Xuerong .

APPLIED MATHEMATICS LETTERS, 2019, 96 :138-146

[7] Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths [J].

Denis, Laurent ;

Hu, Mingshang ;

Peng, Shige .

POTENTIAL ANALYSIS, 2011, 34 (02) :139-161

[8] Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion [J].

Gao, Fuqing .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (10) :3356-3382

[9] 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

[10] On Representation Theorem of G-Expectations and Paths of G-Brownian Motion [J].

Hu, Ming-shang ;

Peng, Shi-ge .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2009, 25 (03) :539-546

← 1 2 3 →