LIMIT PROCESSES FOR AGE-DEPENDENT BRANCHING PARTICLE-SYSTEMS

We consider systems of spatially distributed branching particles in R- d. The particle lifelengths are of general form, hence the time propag ation of the system is typically not Markov. A natural time-spaes-mass scaling is applied to a sequence of particle systems and we derive li mit results for the corresponding sequence of measure-valued processes . The limit is identified as the projection on R-d of a superprocess i n R+ x R-d. 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.