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Convergence Rate for Stable Weighted Branching Processes

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

Abstract

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*.

Keywords

Convergence Rate Stable Distribution Independent Copy Normal Attraction Fixed Point Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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