  Aim of this note is to analyse branching Brownian motion within the class of
models introduced in the recent paper [4] and called chemical diffusion master
equations. These models provide a description for the probabilistic evolution
of chemical reaction kinetics associated with spatial diffusion of individual
particles. We derive an infinite system of Fokker-Planck equations that rules
the probabilistic evolution of the single particles generated by the branching
mechanism and analyse its properties using Malliavin Calculus techniques,
following the ideas proposed in [13]. Another key ingredient of our approach is
the McKean representation for the solution of the
Fisher-Kolmogorov-Petrovskii-Piskunov equation and a stochastic counterpart of
that equation. We also derive the reaction-diffusion partial differential
equation solved by the average concentration field of the branching Brownian
system of particles.
