On boundedness and convergence of solutions for neutral stochastic functional differential equations driven by G-Brownian motion

Abstract

Abstract The current article presents the study of neutral stochastic functional differential equations driven by G-Brownian motion in the phase space Cq((−∞,0];Rn) $C_{q}((-\infty ,0];\mathbb{R}^{n})$. The mean-square boundedness of solutions has been derived. The convergence of solutions with different initial data has been investigated. The boundedness and convergence of solution maps have been obtained. In addition, the LG2 $L^{2}_{G}$ and exponential estimates of solutions have been determined.

Keywords

• Boundedness
• Convergence
• The L G 2 $L^{2}_{G}$ and exponential estimates
• G-Brownian motion
• Neutral stochastic functional differential equations