Branching Process in a Varying Environment: How to Grow Like the Product of Means

Y. Kirpicheva, A. Shklyaev

Consider a branching process $\{Z_n\}$ in a varying environment. Let $\{W_n\}$ be the natural martingale $Z_n/\mathbf{E}{Z}_n$. It converges to some random variable $W$ as $n\to \infty$.…