Girsanov's formula for G-Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Osuka, Emi

关键词: G-Brownian motion;    G-expectation;    Sublinear expectation space;    Girsanov's formula;    Upper expectation;   

DOI  :  10.1016/j.spa.2012.12.009

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

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