This paper studies the mixed zero-sum stochastic differential game problem. We allow functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. show existence solution for this we prove saddle-point game. Moreover, in Markovian framework that value function unique viscosity associated Hamilton–Jacobi–Bellman (H...

We address a zero-sum differential game with ergodic payoff. We study this problem via the viscosity solutions of an associated Hamilton–Jacobi–Isaacs equation. Under certain condition, we establish the existence of a value and prove certain representation formulae.