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 β G (Ω 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.
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Song, Y. Some properties on G-evaluation and its applications to G-martingale decomposition. Sci. China Math. 54, 287–300 (2011). https://doi.org/10.1007/s11425-010-4162-9
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DOI: https://doi.org/10.1007/s11425-010-4162-9