Limiting Distributions in Branching Processes with Two Types of Particles

  • Michael Drmota
  • Vladimir Vatutin
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)


Let us consider a decomposable e branching process with two types of particles T 1, T2 such that particles of type T 2 can only produce particles of types T 1 whereas particles of type T 1 can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T1 and T 2 when the total number n of all particles is fixed. Especially we are interested in the limit case n — ∞. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x 2 distributions, appear.

Key words

branching processes limiting distributions 


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Michael Drmota
    • 1
  • Vladimir Vatutin
    • 2
  1. 1.Department of Discrete MathematicsTechnical University of ViennaViennaAustria
  2. 2.Steklov Mathematical InstituteMoscow, GSP-1Russia

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