论文标题
随机环境中二项式灾难模型的无效复发和瞬态
Null recurrence and transience for a binomial catastrophe model in random environment
论文作者
论文摘要
我们考虑了一个离散的时间人群模型，每个人都在时间$ n $在时间$ n+1 $的情况下与概率$β_n$独立生存。序列$（β_N）$是I.I.D.并构成我们的随机环境。此外，每次$ n $，我们都会向人口添加$ z_n $个人。序列$（z_n）$也是I.I.D.我们发现无效复发和瞬时条件（NEUTS已经解决了积极复发）。我们将结果应用于特定的$（z_n）$分布和确定性$β$。在马尔可夫链从短暂性到无效的情况下，这种特殊情况显示了$β$的相当不寻常的相变，而没有达到积极的复发。
We consider a discrete time population model for which each individual alive at time $n$ survives independently of everybody else at time $n+1$ with probability $β_n$. The sequence $(β_n)$ is i.i.d. and constitutes our random environment. Moreover, at every time $n$ we add $Z_n$ individuals to the population. The sequence $(Z_n)$ is also i.i.d. We find sufficient conditions for null recurrence and transience (positive recurrence has been addressed by Neuts). We apply our results to a particular $(Z_n)$ distribution and deterministic $β$. This particular case shows a rather unusual phase transition in $β$ in the sense that the Markov chain goes from transience to null recurrence without ever reaching positive recurrence.
