On Representation Theorem of G G-Expectations and Paths
On Representation Theorem of G G-Expectations and Paths
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发表时间：
2009
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通讯作者：
Ming-shang Hu;S. Peng
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作者：
Ming-shang Hu;S. Peng
本文给出了一个非常简单和初等的证明，证明了一个弱紧的概率测度族{P θ：θ ∈ θ}表示一个重要的次线性期望--G-期望E（·）.为了证明Cb（Ω）在自然范数E（|·|).
We give a very simple and elementary proof of the existence of a weakly compact family of prob- ability measures {Pθ : θ ∈ Θ} representing an important sublinear expectation— G-expectation E(·). We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions Lip(Ω) in order to prove that Cb(Ω) belongs to the completion of Lip(Ω) under the natural norm E( |·| ).