On representation theorem of G-expectations and paths of G-Brownian motion
On representation theorem of G-expectations and paths of G-Brownian motion
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DOI：
10.1007/s10255-008-8831-1
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发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
Mingshang Hu;S. Peng
中科院分区：
文献类型：
--
作者：
Mingshang Hu;S. Peng
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ:θ∈ gJ} representing an important sublinear expectation-G-expectation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{E} $$\end{document}[·]. We also give a concrete approximation of a bounded continuous functionX(ω) by an increasing sequence of cylinder functionsLip(Ω) in order to prove thatCb(Ω) belongs to the completion ofLip(Ω) under the natural norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{E} $$\end{document}[| · |].
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ:θ∈ gJ} representing an important sublinear expectation—G-expectation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{E} $$\end{document}[·]. We also give a concrete approximation of a bounded continuous functionX(ω) by an increasing sequence of cylinder functionsLip(Ω) in order to prove thatCb(Ω) belongs to the completion ofLip(Ω) under the natural norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{E} $$\end{document}[| · |].