A representation for functionals of superprocesses via particle picture

A superprocess is a measure valued process arising as the limiting density of an infinite collection of particles undergoing branching and diffusion. It can also be defined as a measure valued Markov process with a specified semigroup. Using the latter definition and explicit moment calculations, Dynkin (1988) built multiple integrals for the superprocess. We show that the multiple integrals of the superprocess defined by Dynkin arise as weak limits of linear additive functionals built on the particle system.