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

Cécile Mailler and Jean-François Marckert

Stochastic Processes and their Applications, 2022, vol. 152, issue C, 339-377

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.

Keywords: Galton–Watson trees; Martingale limit; Functional limit theorems (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.06.010

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