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

Matthias Birkner (), Jochen Geiger () and Götz Kersting ()
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Matthias Birkner: Weierstraß-Institut für Angewandte Analysis und Stochastik
Jochen Geiger: Technische Universität Kaiserslautern, Fachbereich Mathematik
Götz Kersting: Universität Frankfurt, Fachbereich Mathematik

A chapter in Interacting Stochastic Systems, 2005, pp 269-291 from Springer

Abstract: 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.

Keywords: Branching process; random environment; random walk; conditioned random walk; Spitzer's condition; functional limit theorem (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27110-9_12

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DOI: 10.1007/3-540-27110-4_12

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