Girsanov’s formula for G-Brownian motion
Girsanov’s formula for G-Brownian motion
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DOI：
10.1016/j.spa.2012.12.009
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发表时间：
2011-06
影响因子：
1.4
通讯作者：
Emi Osuka
中科院分区：
文献类型：
--
作者：
Emi Osuka
本文建立了G-布朗运动的Girsanov公式。Peng(2007,2008)[7，8]在称为G-期望的次线性期望下，在连续路径空间上构造了G-Brown运动；正如Denis等人(2011)和[2]所得到的，G-期望被表示为关于某一类鞅测度的线性期望的上确界。在经典随机分析中，我们的论点是基于这种表示和相关的一类鞅测度的扩大，并基于格尔萨诺夫的关于鞅的公式。这种方法不同于Xu等人(2011)和[13]的方法，并且适用于多维G-布朗运动。
In this paper, we establish Girsanov’s formula for G-Brownian motion. Peng (2007, 2008) [7,8] constructed G-Brownian motion on the space of continuous paths under a sublinear expectation called G-expectation; as obtained by Denis et al. (2011) [2], 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) [13], and applies to the multidimensional G-Brownian motion.