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.

中文翻译：

---

G-布朗运动的吉尔萨诺夫定理：退化情况

在本文中，我们证明了 G-布朗运动的 Girsanov 定理在没有非退化条件的情况下。该证明基于非线性设置中的微扰方法，通过构造 G 期望空间和包含标准布朗运动的线性空间的乘积空间。G-布朗运动的指数鞅的估计对我们的论点很重要。