Emi Osuka
Published 2011-06-13, updated 2013-02-21Version 3
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 multi-dimensional $G$-Brownian motion.
Journal: Stochastic Processes and their Applications, Volume 123, Issue 4, April 2013, Pages 1301--1318
An Iterative Approximation of the Sublinear Expectation of an Arbitrary Function of $G$-normal Distribution and the Solution to the Corresponding $G$-heat Equation
On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion
Sublinear expectations for countable-state uncertain processes
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