Backward equations, stochastic control and zero-sum stochastic differential games

This paper is concerned with the applications to stochastic control and stochastic zero-sum differential games of some results on backward stochastic differential equations. Using these techniques we give a new approach of the existence of an optimal strategy for the stochastic control of diffusions; in a same way we prove the existence of a saddle-point for zero-sum stochastic differential games when the Isaacs' condition is satisfied