论文标题
几乎关键的加尔顿 - 沃森流程
Nearly critical Galton--Watson processes
论文作者
论文摘要
我们研究了Galton - Watson在不同环境中的过程，$ \ bar f_n \ uparrow 1 $和$ \ sum_ {n = 1}^\ infty（1- \ bar f_n）= \ infty $，其中$ \ bar f_n $代表offspring代表$ n $ n $ n $ n $ n $。由于该过程几乎可以肯定地消失，因此，为了获得非平凡的限制，我们考虑两种情况：根据非灭绝或增加移民的条件。在这两种情况下，我们都表明，该过程在分布中收敛，而无需标准化与非化合物 - 散异的限制定律。证明依赖于形状功能技术，由Kersting（2020）制定。
We investigate Galton--Watson processes in varying environment, for which $\bar f_n \uparrow 1$ and $\sum_{n=1}^\infty (1-\bar f_n) = \infty$, where $\bar f_n$ stands for the offspring mean in generation $n$. Since the process dies out almost surely, to obtain nontrivial limit we consider two scenarios: conditioning on non-extinction, or adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting (2020).
