Abstract
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.
Highlights
Stochastic differential equations (SDEs) have been used profitably in a variety of fields including population dynamics, engineering, environments, physics and medicine
One cannot obtain the explicit solutions to Neutral stochastic functional differential equations (NSFDEs)
The mean square stability is developed for the above-mentioned stochastic differential equations
Summary
Stochastic differential equations (SDEs) have been used profitably in a variety of fields including population dynamics, engineering, environments, physics and medicine. SDEs are utilized in the field of finance as they are optimal to modern finance theory and have been broadly employed to model the behavior of key variables; the variables include the asset returns, asset prices, instantaneous short-term interest rate and their volatility Biologists use these equations to model the achievement of stochastic changes in reproduction on population processes [ , ]. By virtue of linear growth and Lipschitz conditions, the existence theory for the solutions to neutral stochastic functional differential equations in the G-framework (G-NSFDEs) was given by Faizullah [ ]. These equations depend on the present and past data and depend on the rate of change of the past data [ , ].
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