Existence and stability of solutions to non-linear neutral stochastic functional differential equations in the framework of G-Brownian motion

In the past decades, quantitative study of different disciplines such as system sciences, physics, ecological sciences, engineering, economics and biological sciences, have been driven by new modeling known as stochastic dynamical systems. This paper aims at studying these important dynamical systems in the framework of G-Brownian motion and G-expectation. It is demonstrated that, under the contractive condition, the weakened linear growth condition and the non-Lipschitz condition, a neutral stochastic functional differential equation in the G-frame has at most one solution. Hölder’s inequality, Gronwall’s inequality, the Burkholder-Davis-Gundy (in short BDG) inequalities, Bihari’s inequality and the Picard approximation scheme are used to establish the uniqueness-and-existence theorem. In addition, the stability in mean square is developed for the above mentioned stochastic dynamical systems in the G-frame.

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