Persistence of critical multitype particle and measure branching processes |
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Authors: | L. G. Gorostiza S. Roelly A. Wakolbinger |
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Affiliation: | (1) Centro de Investigación y de Estudios Avanzados, Ap.Postal 14-740, 07000 México, D.F., México;(2) Laboratoire de Probabilités, Université Paris VI 4, Place Jussieu, Tour 56-3emeEtage, UA C.N.R.S. 0224, F-75252 Paris Cedex 05, France;(3) Institut für Mathematik, Johannes Kepler Universität Linz, A-4040 Linz, Austria |
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Abstract: | Summary We consider a class of systems of particles ofk types inRd undergoing spatial 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.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria). |
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