Martingale Property and Capacity under G-Framework

Jing Xu (School of Economics and Business Administration)
Bo Zhang (School of Statistics Renmin University of China)

Abstract


The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. http://arxiv.org/PS_cache/math/pdf/0601/0601035v2.pdf) in 2006. We show that the G-capacity can not be dynamic, and also demonstrate the relationship between symmetric G-martingale and the martingale under linear expectation. Based on these results and path-wise analysis, we obtain the martingale characterization theorem for G Brownian motion without Markovian assumption. This theorem covers the Levy's martingale characterization theorem for Brownian motion, and it also gives a different method to prove Levy's theorem.

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Pages: 2041-2068

Publication Date: December 3, 2010

DOI: 10.1214/EJP.v15-832

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