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Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game Problem with Payoff Functional in BDSDES

In this paper, we study stochastic recursive (mixed) zero-sum differential game and this game problem’ payoff functional is depicted by the forms of a backward doubly stochastic differential equation'solution. The major means are backward doubly stochastic differential equations (BDSDEs) and double-barrier reflected BDSDEs.in such case, we confirmed the truth of that a saddle point of the stochastic recursive differential game problem above-mentioned is existed and obtained the optimal payoff functional.