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In this article, a notion of viscosity solutions is introduced for fully nonlinear second order path-dependent partial differential equations in the spirit of Zhou, Ann. Appl. Probab., 33 (2023), 5564-5612. We prove the existence, comparison principle, consistency and stability for the viscosity solutions. Application to path-dependent stochastic differential games is given.
Tang et al. (Fri,) studied this question.