Existence and uniqueness of solutions to SFDEs driven by G-Brownian motion with non-Lipschitz conditions.

The main aim of this paper is to study the existence, uniqueness and stability of solution for stochastic functional differential equations driven by G-Brownian motion (in short G-SFDEs). The existence-and-uniqueness theorem is established for G-SFDEs under non-Lipschitz condition and weakened linear growth condition. We have used the Picard approximation scheme, Gronwall's inequality, Bihari's inequality and Burkholder-Davis-Gundy (in short BDG) inequalities to develop the existence theory for the above mentioned stochastic dynamical systems. In addition, the mean square stability of solutions for these systems has been obtained. [ABSTRACT FROM AUTHOR]