Parametrised branching processes: a functional version of Kesten \& Stigum theorem

Cécile Mailler, Jean-François Marckert

Let $(Z_n,n\ge 0)$ be a supercritical Galton-Watson process whose offspring distribution $\mu$ has mean $\lambda >1$ and is such that $\int x(\log (x){)}_{+}d\mu (x)<+\infty$. According to the fa…