论文标题
随机环境中的亚临界分支过程与移民：单个家庭的生存
Subcritical branching processes in random environment with immigration: survival of a single family
论文作者
论文摘要
我们考虑I.I.D.中的亚临界分支过程随机环境，其中一个移民到达每一代。我们认为活动$％\ Mathcal {a} _ {i}（n）$，所有在时间$ n $都活着的人都是移民的后代，该移民在时间$ i $上加入了人口，并调查了此极端事件的渐近概率，当$ n \ to \ iftty $和$ i $ are nive of nives of nive $ n-i是$ n-i $ n-i是$ n-i $ n-i是$ n-i $ n-i $ n-i是$ n-i $ n-i $ n-i是$ n-i $ n-i $ n-i $ n--i $ \ min（i，n-i）\ to \ infty。$为了推断所需的渐近学，我们为随机步行而建立了一些限制定理，以无效或负数为条件。
We consider a subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the immigrant which joined the population at time $i$ and investigate the asymptotic probability of this extreme event when $n\to\infty$ and $i$ is either fixed, or the difference $n-i$ is fixed, or $\min(i,n-i)\to\infty.$ To deduce the desired asymptotics we establish some limit theorems for random walks conditioned to be nonnegative or negative.
