A probabilistic representation for the solutions to some non-linear PDEs   using pruned branching trees
  The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of the stochastic representation, using a companion scalar PDE.   In cases where the representation fails to be integrable a sequence of pruned trees is constructed, producing a approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE. 
D. Bl\"omker, M. Romito, R. Tribe