Fluctuations of spatial branching processes with mean-field interaction

We consider a branching Brownian motion on starting with n particles of mass 1/n, with interactive branching dynamics. The parameters are unsealed, but depend on the present state of the measure-valued process. For this mean-field model, which is a generalization of Chauvin and Rouault (1990) and Nappo and Orlandi (1988), we prove a propagation of chaos and a fluctuation theorem in ([0, T]; W.5).