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An integral test for a critical multitype spatially homogeneous branching particle process and a related reaction-diffusion system
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  • Published: April 2000

An integral test for a critical multitype spatially homogeneous branching particle process and a related reaction-diffusion system

  • Klaus Fleischmann1 &
  • Vladimir A. Vatutin1 

Probability Theory and Related Fields volume 116, pages 545–572 (2000)Cite this article

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  • 4 Citations

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Abstract.

An integral test (Theorem 5) is established for the dichotomy concerning local extinction and survival (even persistence) at late times for critical multitype spatially homogeneous branching particle systems in continuous time. Our conditions on the branching mechanism are close to the ones known from “classical” processes without motion component. This generalizes and complements results of López-Mimbela and Wakolbinger [LMW96] and others. Our approach is based on some genealogical tree analysis combined with the study of the long-term behavior of L 1-norms of solutions of related systems of reaction-“diffusion” equations, which is perhaps also of some independent interest.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, D-10117 Berlin, Germany. e-mail: fleischmann@wias-berlin.de, , , , , , DE

    Klaus Fleischmann & Vladimir A. Vatutin

Authors
  1. Klaus Fleischmann
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  2. Vladimir A. Vatutin
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Received: 13 August 1997 / Revised version: 12 May 1998 / Published online: 14 February 2000

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Fleischmann, K., Vatutin, V. An integral test for a critical multitype spatially homogeneous branching particle process and a related reaction-diffusion system. Probab Theory Relat Fields 116, 545–572 (2000). https://doi.org/10.1007/s004400050262

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  • Issue Date: April 2000

  • DOI: https://doi.org/10.1007/s004400050262

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Keywords

  • Late Time
  • Continuous Time
  • Tree Analysis
  • Particle System
  • Related System
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