Stochastic Functional Differential Equations Driven By G-Brownian Motion

In this paper, we mainly consider stochastic functional differential equations driv-en by G—Brownian motion in the framework of sublinear expectation space (Ω, H, E). Firstly, we prove the existence and uniqueness of the solutions to the stochastic func-tional differential equations driven by G-Brownian motion with the coefficients sat-isfying the linear growth condition and the local Lipschitz condition. Secondly, we establish the moment estimate, exponential estimate and continuity of the solution. Fi-nally, we discuss the stability of the solution, and show moment exponential stability and quasi surely exponential stability.