## Electronic Journal of Probability

### Martingale Property and Capacity under G-Framework

#### Abstract

The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. <a href="http://arxiv.org/PS_cache/math/pdf/0601/0601035v2.pdf">http://arxiv.org/PS_cache/math/pdf/0601/0601035v2.pdf</a>) 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.

#### Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 67, 2041-2068.

Dates
Accepted: 3 December 2010
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819852

Digital Object Identifier
doi:10.1214/EJP.v15-832

Mathematical Reviews number (MathSciNet)
MR2745725

Zentralblatt MATH identifier
1226.60085

Subjects
Primary: 60H05: Stochastic integrals

Rights

#### Citation

Xu, Jing; Zhang, Bo. Martingale Property and Capacity under G-Framework. Electron. J. Probab. 15 (2010), paper no. 67, 2041--2068. doi:10.1214/EJP.v15-832. https://projecteuclid.org/euclid.ejp/1464819852

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