Parametrised branching processes: a functional version of Kesten & Stigum theorem
Parametrised branching processes: a functional version of Kesten & Stigum theorem
Let $(Z_n,n\geq 0)$ be a supercritical Galton-Watson process whose offspring distribution $\mu$ has mean $\lambda>1$ and is such that $\int x(\log(x))_+ d\mu(x) 1$ for all $\lambda\in I$. This allows us to define $Z_n(\lambda)$ the number of elements in the $n$th generation at time $\lambda$. Set $W_n(\lambda)= Z_n(\lambda)/\lambda^n$ for all $n\geq …