Stopping times and related Itô's calculus with G-Brownian motion

Under the framework of G-expectation and G-Brownian motion, we introduce Itô's integral for stochastic processes without assuming quasi-continuity. Then we can obtain Itô's integral on stopping time interval. This new formulation permits us to obtain Itô's formula for a general C1,2-function, which essentially generalizes the previous results of Peng (2006, 2008, 2009, 2010, 2010) [21], [22], [23], [24] and [25] as well as those of Gao (2009) [8] and Zhang et al. (2010) [27].