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Branching Processes in Random Environment — A View on Critical and Subcritical Cases

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Interacting Stochastic Systems

Summary

Branching processes exhibit a particularly rich longtime behaviour when evolving in a random environment. Then the transition from subcriticality to supercriticality proceeds in several steps, and there occurs a second ‘transition’ in the subcritical phase (besides the phase-transition from (sub)criticality to supercriticality). Here we present and discuss limit laws for branching processes in critical and subcritical i.i.d. environment. The results rely on a stimulating interplay between branching process theory and random walk theory. We also consider a spatial version of branching processes in random environment for which we derive extinction and ultimate survival criteria.

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Author information

Authors and Affiliations

  1. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117, Berlin, Germany

    Matthias Birkner

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Jochen Geiger

  3. Fachbereich Mathematik, Universität Frankfurt, Fach 187, D-60054, Frankfurt am Main, Germany

    Götz Kersting

Authors
  1. Matthias Birkner
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  2. Jochen Geiger
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  3. Götz Kersting
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Editor information

Editors and Affiliations

  1. Fakultät II, Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Jean-Dominique Deuschel

  2. Fachbereich Mathematik und Physik Mathematisches Institut, Universität Erlangen, Bismarckstr. 1 1/2, 91054, Erlangen, Germany

    Andreas Greven

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Birkner, M., Geiger, J., Kersting, G. (2005). Branching Processes in Random Environment — A View on Critical and Subcritical Cases. In: Deuschel, JD., Greven, A. (eds) Interacting Stochastic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27110-4_12

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