  We present an algorithm for the numerical solution of nonlinear parabolic
partial differential equations. This algorithm extends the classical
Feynman-Kac formula to fully nonlinear partial differential equations, by using
random trees that carry information on nonlinearities on their branches. It
applies to functional, non-polynomial nonlinearities that are not treated by
standard branching arguments, and deals with derivative terms of arbitrary
orders. A Monte Carlo numerical implementation is provided.
