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 ξ∈ L β G (Ω T ) with some β > 1 the mart...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 ξ∈ 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 Ito 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.展开更多
基金supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814902)
文摘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 ξ∈ 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 Ito 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.
