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

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

2009-04-29

arxiv.org/abs/0904.4519v1

Mathematics

Probability

12 pages

Scientific paper

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures $\{P_{\theta}:\theta \in \Theta \}$ to represent an important sublinear expectation--G-expectation $\mathbb{E}[\cdot]$. We also give a concrete approximation of a bounded continuous function $X(\omega)$ by an increasing sequence of cylinder functions $L_{ip}(\Omega)$ in order to prove that $C_{b}(\Omega)$ belongs to the $\mathbb{E}[|\cdot|]$-completion of the $L_{ip}(\Omega)$.

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