Girsanov Theorem for G-Brownian Motion: The Degenerate Case

In this paper, we prove the Girsanov theorem for G -Brownian motion without the non-degenerate condition. The proof is based on the perturbation method in the nonlinear setting by constructing a product space of the G -expectation space and a linear space that contains a standard Brownian motion. The estimates for exponential martingales of G -Brownian motion are important for our arguments.