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, and Zhang [Ann. Probab., 44 (2016), pp. 2507{2553], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the reg- ularization method as introduced by Jensen, Lions, and Souganidis [Proc. Amer. Math. Soc., 102, (1988)] in the corresponding finite-dimensional PDE setting. The present argument significantly sim-plifies the comparison proof of Ekren, Touzi, and Zhang but requires an Lp-type of continuity (with respect to the path) for the viscosity semisolutions and for the nonlinearity defining the equation.