On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion
Abstract
Description
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures $\{P_θ:θ\in Θ\}$ to represent an important sublinear expectation--G-expectation $\mathbb{E}[\cdot]$. We also give a concrete approximation of a bounded continuous function $X(ω)$ by an increasing sequence of cylinder functions $L_{ip}(Ω)$ in order to prove that $C_{b}(Ω)$ belongs to the $\mathbb{E}[|\cdot|]$-completion of the $L_{ip}(Ω)$.
12 pages
12 pages