Abstract
ABSTRACTThis 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 . 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.
Highlights
The stochastic differential equations (SDEs) theory has been used in several disciplines of sciences and engineering
By virtue of the growth and Lipschitz conditions, SDEs in the framework of G-Brownian motion were studied by Peng [4,5]
We investigate the Euler-Maruyama approximation procedure for SDEs in the framework of G-Browinian motion with non-linear growth and nonLipschitz conditions
Summary
The stochastic differential equations (SDEs) theory has been used in several disciplines of sciences and engineering. By virtue of the growth and Lipschitz conditions, SDEs in the framework of G-Brownian motion were studied by Peng [4,5]. He derived the existence and uniqueness results in view of the contraction principle technique. We investigate the Euler-Maruyama approximation procedure for SDEs in the framework of G-Browinian motion with non-linear growth and nonLipschitz conditions. This section gives estimates for the difference between an exact solution Z(t) and approximate solutions Zq(t) of SDEs in the framework of G-Brownian motion
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