Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs

We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang [10], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the regularization method as introduced by Jensen, Lions & Souganidis [11] in the corresponding finite-dimensional PDE setting. The present argument significantly simplifies the comparison proof in [10], but requires an L−type of continuity (with respect to the path) for the viscosity semi-solutions and for the nonlinearity defining the equation.