Approximation and representation of the value for some differential games with imperfect information

We consider differential games with imperfect information. For special games with dynamics independent of the state of the system and linear payoffs, we give a representation formula for the value similar to the value of repeated games with lack of information on both sides. For general games, this representation formula does not hold and we introduce an approximation of the value : we build a sequence of functions converging to the value function.