ASYMPTOTICS OF THE DISTRIBUTION AND HARMONIC MOMENTS FOR A SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT
Résumé
Let $(Z_n)$ be a supercritical branching process in an independent and identically distributed random environment $\xi$.
We deduce the exact decay rate of the probability $P(Z_n=j | Z_0 = k)$ as $n \to \infty$, for each $j \geq k,$ assuming that $\p (Z_1 = 0) =0$. We also study the existence of harmonic moments of the random variable $W=\lim_{n\rightarrow \infty}\frac{Z_n}{ E (Z_n|\xi)}$ under a simple moment condition.
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