2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120740The 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.ProbabilityMathematical Physics60J80; 35Q30; 35K55; 35C99; 76M35; 60H30text