On Representation Theorem of G-Expectations and Paths of G-Brownian Motion  

作　　者：Ming-shang Hu Shi-ge Peng 

机构地区：[1]Institute of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第3期539-546,共8页应用数学学报（英文版）

基　　金：support from The National Basic Research Program of China(973 Program)grant No.2007CB814900(Financial Risk)

摘　　要：We give a very simple and elementary proof of the existence of a weakly compact family of probability 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[｜·｜].We give a very simple and elementary proof of the existence of a weakly compact family of probability 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[｜·｜].

关 键 词：Probability and distribution uncertainty G-normal distribution G-Brownian motion continuous paths 

分 类 号：O159[理学—数学] O211.67[理学—基础数学]