Weak Approximation of G-Expectations
  We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion. 
Yan Dolinsky, Marcel Nutz, H. Mete Soner
math.PR math.OC