Summary
We consider a class of systems of particles ofk types inR d 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”.
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Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).
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Gorostiza, L.G., Roelly, S. & Wakolbinger, A. Persistence of critical multitype particle and measure branching processes. Probab. Th. Rel. Fields 92, 313–335 (1992). https://doi.org/10.1007/BF01300559
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DOI: https://doi.org/10.1007/BF01300559
Keywords
- Stochastic Process
- Probability Theory
- General Class
- Mathematical Biology
- Particle System