  It is known that Markovian forward-backward stochastic differential equations
provide nonlinear Feynman-Kac representation formulae for semilinear parabolic
PDEs. We show that non-Markovian forward-backward stochastic differential
equations provide nonlinear Feynman-Kac formulae for semilinear path-dependent
PDEs. This extends the result proved in Ekren, Keller, Touzi, and Zhang [4] to
the case with a possibly degenerate diffusion coefficient in the forward
dynamics.
