In this paper, we establish Girsanov's formula for G-Brownian motion. Peng (2007, 2008) constructed G-Brownian motion on the space of continuous paths under a sublinear expectation called G-expectation; as obtained by Denis et al. (2011), G-expectation is represented as the supremum of linear expectations with respect to martingale measures of a certain class. Our argument is based on this representation with an enlargement of the associated class of martingale measures, and on Girsanov's formula for martingales in the classical stochastic analysis. The methodology differs from that of Xu et al. (2011), and applies to the multidimensional G-Brownian motion.

The purpose of this paper is to establish a variational representationHere E is a sublinear expectation called G-expectation, f is any bounded function in the domain of E mapping C([0, 1]; R d ) to R, the integrals are taken with respect to the quadratic variation of B, and the supremum runs over all h's for which these integrals are well-defined. As an application, we give another proof of the results obtained by Gao-Jiang (2010), large deviations for G-Brownian motion.