We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,F) but introduce probability measures by means of Girsanov’s transformation depending on the policies of the players. We also show that the value function does not change if we allow...

We prove the dynamic programming principle for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order “coefficient” and the “free” term are only assumed to be...