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

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 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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Correspondence to YongSheng Song.

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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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Keywords

  • G-expectation
  • G-evaluation
  • G-martingale
  • decomposition theorem

MSC(2000)

  • 60G07
  • 60G20
  • 60G44
  • 60G48
  • 60H05