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This paper explores the relationship between non-Markovian fully coupledforward-backward stochastic systems and path-dependent PDEs. The definition ofclassical solution for the path-dependent PDE is given within the framework offunctional It\^{o} calculus. Under mild hypotheses, we prove that theforward-backward stochastic system provides the unique classical solution tothe path-dependent PDE.

Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs