Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework. Issue 1 (11th December 2019)

• Record Type: Journal Article
• Authors: Faizullah, Faiz; Khan, Ilyas; Salah, Mukhtar M.; Alhussain, Ziyad Ali
• Is Part Of: Journal of Taibah University for science. Volume 13:Issue 1(2019)
• Page Start: 20
• Page End: 26
• Publication Date: 2019-12-11
• Subjects: G-Brownian motion -- stochastic differential equations -- non-linear growth and non-Lipschitz conditions -- estimates -- bounded solutions; 60H20 -- 60H10 -- 60H35 -- 62L20; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2018.1519884
• Languages: English
• ISSNs: 1658-3655

Abstract

ABSTRACT: 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), Hölder'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 M G 2 ( [ t 0, T ] ; R n ) . In view of non-linear growth and non-uniform Lipschitz conditions, we give estimates for the difference between the exact solution Z ( t ) and approximate solutions Z q ( t ) of SDEs in the framework of G-Brownian motion.