Verification Theorem of Stochastic Recursive Optimal Control Problems with Mixed Delay for Viscosity Solutions

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This paper is concerned with a kind of stochastic recursive optimal control problem with mixed delay. In the framework of viscosity solutions, stochastic verification theorem is proved. Furthermore, we find that the usual additional regularity assumptions are not necessary, which first were imposed on the viscosity solution to the HJB equation in Gozzi, Swiech and Zhou [20], as a supplementary assumption for the classical stochastic verification theorem. Hence we obtain a verification theorem under weaker assumptions.