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

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];\mathbb {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.

Keywords

• g-brownian motion
• stochastic differential equations
• non-linear growth and non-lipschitz conditions
• estimates
• bounded solutions