A Complete Representation Theorem for $G$-martingales
  In this paper we establish a complete representation theorem for $G$-martingales. Unlike the existing results in the literature, we provide the existence and uniqueness of the second order term, which corresponds to the second order derivative in Markovian case. The main ingredient of the paper is a new norm for that second order term, which is based on an operator introduced by Song [26]. 
Shige Peng, Yongsheng Song, Jianfeng Zhang
math.PR