WIAS Preprint No. 306, (1996)

Reduced subcritical Galton-Watson processes in a random environment



Authors

  • Fleischmann, Klaus
  • Vatutin, Vladimir A.

2010 Mathematics Subject Classification

  • 60J80 60J15

Keywords

  • Branching process in a random environment, random walk in a random environment, reduced process, reduced tree, conditional limit theorem, age of the most recent common ancestor, source time, hybrid behavior

Abstract

We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (in time randomly varying) offspring generating functions are fractional linear. We show that this structure may differ significantly from that for the "classical" reduced subcritical Galton-Watson processes. In particular, it may look like a complex "hybrid" of classical reduced super- and subcritical processes. Some relations with random walks in a random environment are discussed.

Appeared in

  • Adv. Appl. Probab. 31(1) (1999), pp. 88-111

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