Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework

被引：3

作者：

Faizullah, Faiz ^{[1
,2
]}

Khan, Ilyas ^{[3
,4
,5
]}

Salah, Mukhtar M. ^{[4
,5
]}

Alhussain, Ziyad Ali ^{[5
]}

机构：

[1] Swansea Univ, Dept Math, Swansea, W Glam, Wales

[2] NUST, Dept Basic Sci & Humanities, Coll Elect & Mech Engn, Islamabad, Pakistan

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[4] Majmaah Univ, Coll Engn, Basic Engn Sci Dept, Majmaah, Saudi Arabia

[5] Majmaah Univ, Coll Sci, Dept Math, Majmaah, Saudi Arabia

来源：

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2019年 / 13卷 / 01期

关键词：

G-Brownian motion; stochastic differential equations; non-linear growth and non-Lipschitz conditions; estimates; bounded solutions; G-BROWNIAN MOTION; DRIVEN; EXISTENCE; UNIQUENESS; CALCULUS; TIMES;

D O I：

10.1080/16583655.2018.1519884

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. The results are derived by using the Burkholder-Davis-Gundy (in short BDG), Holder's, Doobs martingale's and Gronwall's inequalities. Subject to non-linear growth condition, it is revealed that the Euler-Maruyama approximate solutions are bounded in . In view of non-linear growth and non-uniform Lipschitz conditions, we give estimates for the difference between the exact solution and approximate solutions of SDEs in the framework of G-Brownian motion.

引用

页码：20 / 26

页数：7

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