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Science China Mathematics

, Volume 54, Issue 2, pp 287–300 | Cite as

Some properties on G-evaluation and its applications to G-martingale decomposition

  • YongSheng Song
Articles

Abstract

In this article, a sublinear expectation induced by G-expectation is introduced, which is called G-evaluation for convenience. As an application, we prove that for any ζ ∈ L G β T ) with some β > 1 the martingale decomposition theorem under G-expectaion holds, and that any β > 1 integrable symmetric G-martingale can be represented as an Itô integral w.r.t. G-Brownian motion. As a byproduct, we prove a regularity property for G-martingales: Any G-martingale {M t } has a quasi-continuous version.

Keywords

G-expectation G-evaluation G-martingale decomposition theorem 

MSC(2000)

60G07 60G20 60G44 60G48 60H05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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