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Parameterised branching processes: A functional version of Kesten & Stigum theorem

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  • Mailler, Cécile
  • Marckert, Jean-François

Abstract

Let (Zn,n≥0) be a supercritical Galton–Watson process whose offspring distribution μ has mean λ>1 and is such that ∫xlog+(x)dμ(x)<+∞. According to the famous Kesten & Stigum theorem, (Zn/λn) converges almost surely, as n→+∞. The limiting random variable has mean 1, and its distribution is characterised as the solution of a fixed point equation.

Suggested Citation

  • Mailler, Cécile & Marckert, Jean-François, 2022. "Parameterised branching processes: A functional version of Kesten & Stigum theorem," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 339-377.
    • Handle: RePEc:eee:spapps:v:152:y:2022:i:c:p:339-377
    DOI: 10.1016/j.spa.2022.06.010
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    References listed on IDEAS

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    1. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
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