Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion

This paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the solution for locally Lipschitz GSDEs are obtained by localization methods, also the stability of such GSDEs is discussed with Lyapunov-type conditions.