PERSISTENCE OF CRITICAL MULTITYPE PARTICLE AND MEASURE BRANCHING-PROCESSES

We consider a class of systems of particles of k types in R(d) undergoing spatiai diffusion and critical multitype branching, where the diffusions, the particle lifetimes and the branching laws depend on the types. We prove persistence criteria for such systems and for their corresponding high density limits known as multitype Dawson-Watanabe processes. The main tool is a representation of the Palm distributions for a general class of inhomogeneous critical branching particle systems, constructed by means of a "backward tree".