Girsanov’s formula for GG-Brownian motion

In this paper, we establish Girsanov’s formula for GG-Brownian motion. Peng (2007, 2008) [7] and [8] constructed GG-Brownian motion on the space of continuous paths under a sublinear expectation called GG-expectation; as obtained by Denis et al. (2011) [2], GG-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) [13], and applies to the multidimensional GG-Brownian motion.