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Persistence of critical multitype particle and measure branching processes
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  • Published: September 1992

Persistence of critical multitype particle and measure branching processes

  • L. G. Gorostiza1,
  • S. Roelly2 &
  • A. Wakolbinger3 

Probability Theory and Related Fields volume 92, pages 313–335 (1992)Cite this article

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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Author information

Authors and Affiliations

  1. Centro de Investigación y de Estudios Avanzados, Ap.Postal 14-740, 07000, México, D.F., México

    L. G. Gorostiza

  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

    S. Roelly

  3. Institut für Mathematik, Johannes Kepler Universität Linz, A-4040, Linz, Austria

    A. Wakolbinger

Authors
  1. L. G. Gorostiza
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  2. S. Roelly
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  3. A. Wakolbinger
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Additional information

Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).

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Cite this article

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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  • Received: 26 November 1990

  • Revised: 11 November 1991

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01300559

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Keywords

  • Stochastic Process
  • Probability Theory
  • General Class
  • Mathematical Biology
  • Particle System
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