%0 Journal Article
%T Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework
%A Faiz Faizullah
%A Ilyas Khan
%A Mukhtar M. Salah
%A Ziyad Ali Alhussain
%J Journal of Taibah University for Science
%D 2019
%R https://doi.org/10.1080/16583655.2018.1519884
%X 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), H£żlder'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
%U https://www.tandfonline.com/doi/full/10.1080/16583655.2018.1519884