Representation Formula for Viscosity Solutions to a class of Nonlinear Parabolic PDEs

We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDEs given as a sup–envelope function. This is done through a dynamic programming principle derived from Denis, Hu, Peng (2010). The formula can be seen as a nonlinear extension of the Feynman–Kac formula and is based on the backward stochastic differential equations theory.