Limit value of dynamic zero-sum games with vanishing stage duration

We consider two person zero-sum games where the players control, at discrete times {tn} induced by a partition $\Pi$ of R + , a continuous time Markov state process. We prove that the limit of the values v$\Pi$ exist as the mesh of $\Pi$ goes to 0. The analysis covers the cases of : 1) stochastic games (where both players know the state) 2) symmetric no information. The proof is by reduction to a deterministic differential game.