  In this paper, BDG-type inequality for G-stochastic calculus with respect to
G-Levy process is obtained and solutions of stochastic differential equations
driven by G-Levy process under non-Lipschitz condition are constructed.
Moreover, we establish the mean square exponential stability and quasi sure
exponential stability of the solutions be means of G-Lyapunov function method.
An example is presented to illustrate the efficiency of the obtained results.
