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Variational characterization of multitype Galton-Watson branching processes

  • Ying WangEmail author
Article

Abstract

In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.

Keywords

multitype branching processes retrospective processes variational analysis equilibrium states large deviations 

2000 MR Subject Classification

60J80 90C46 15A18 

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Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  3. 3.Warwick Systems Biology CentreUniversity of WarwickCoventryUK

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