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2010 Martingale Property and Capacity under G-Framework
Jing Xu, Bo Zhang
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Electron. J. Probab. 15: 2041-2068 (2010). DOI: 10.1214/EJP.v15-832

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.

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Jing Xu. Bo Zhang. "Martingale Property and Capacity under G-Framework." Electron. J. Probab. 15 2041 - 2068, 2010. https://doi.org/10.1214/EJP.v15-832

Information

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

zbMATH: 1226.60085
MathSciNet: MR2745725
Digital Object Identifier: 10.1214/EJP.v15-832

Subjects:
Primary: 60H05
Secondary: 60H10

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Vol.15 • 2010
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