Limit Processes for Age-Dependent Branching Particle Systems

We consider systems of spatially distributed branching particles in Rd. The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on Rd of a superprocess in R+×Rd. The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles.