论文标题
限制在随机环境中超临界分支过程的定理
Limit theorems for supercritical branching processes in random environment
论文作者
论文摘要
我们考虑随机环境中的分支过程$ \ {z_n \} _ {n \ geq 0} $，这是一个〜人口增长过程，个人在每个世代随机选择的复制法。当过程以积极的概率生存并在无Xt缩合集上成倍增长时，我们将重点放在超临界情况下。我们的主要目标是为该模型建立傅立叶技术，该技术允许获得许多与限制定理有关的精确估计。结果，我们提供有关中央限制定理，Edgeworth扩展和续订定理的新结果。
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus on the supercritical case, when the process survives with a positive probability and grows exponentially fast on the nonextinction set. Our main is goal is establish Fourier techniques for this model, which allow to obtain a number of precise estimates related to limit theorems. As a consequence we provide new results concerning central limit theorem, Edgeworth expansions and renewal theorem for $\log Z_n$.
