Convergence Rate for Stable Weighted Branching Processes

  • Rösler Uwe
  • Topchii Valentin
  • Vatutin Vladimir
Conference paper
Part of the Trends in Mathematics book series (TM)


Let the martingale Wn= m−n Zn where Zn is a weighted branching process and \(m = E{\sum _j}{T_j}\) is the expected sum of the random factors Tj converge to a limiting random variable W. We give conditions in terms of the factors under which W belongs to the domain of attraction or to the domain of normal attraction of an α-stable distribution with 1 < α ≤ 2. The convergence rate of Wn to W is evaluated in the sense that correctly normalized converges to a nondegenerate random variable*.


Convergence Rate Stable Distribution Independent Copy Normal Attraction Fixed Point Equation 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Rösler Uwe
    • 1
  • Topchii Valentin
    • 2
  • Vatutin Vladimir
    • 3
  1. 1.Mathematisches SeminarderChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Omsk Branch of Sobolev Institute of MathematicsOmskRussia
  3. 3.Steklov Mathematical InstituteMoscowRussia

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