In this paper, we establish Girsanov's formula for $G$-Brownian motion. Peng(2007, 2008) constructed $G$-Brownian motion on the space of continuous pathsunder a sublinear expectation called $G$-expectation; as obtained by Denis etal. (2011), $G$-expectation is represented as the supremum of linearexpectations with respect to martingale measures of a certain class. Ourargument is based on this representation with an enlargement of the associatedclass of martingale measures, and on Girsanov's formula for martingales in theclassical stochastic analysis. The methodology differs from that of Xu et al.(2011), and applies to the multi-dimensional $G$-Brownian motion.
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机译：在本文中，我们建立了Girsanov的$ G $-布朗运动公式。 Peng（2007，2008）在一个称为$ G $ -expectation的亚线性期望下，在连续路径的空间上构造了$ G $ -Brownian运动。由Denis等人获得。 （2011年），$ G $ -expectation表示某类mar度量的线性期望的最高值。我们的论点是基于这种表示法，并扩大了mar度量的相关类，并且基于经典随机分析中吉尔萨诺夫的mar公式。该方法与Xu等人（2011）的方法不同，适用于多维$ G $-布朗运动。
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