  The aim of this paper is to present the analysis for the solutions of
nonlinear stochastic functional differential equation driven by G-Brownian
motion with infinite delay (G-SFDEwID). Under some useful assumptions, we have
proved that the G-SFDEwID admits a unique local solution. The mentioned theory
has been further generalized to show that G-SFDEwID admits a unique strong
global solution. The asymptotic properties, mean square boundedness and
convergence of solutions with different initial data have been derived. We have
assessed that the solution map $X_t$ is mean square bounded and two solution
maps from different initial data are convergent. In addition, the exponential
estimate for the solution has been studied.
