论文标题
限制在随机环境中移民的分支过程的定理
Limit Theorems for Branching Processes with Immigration in a Random Environment
论文作者
论文摘要
我们研究了在随机环境中移民的亚临界加尔顿 - 瓦特森分支过程。使用Goldie的隐式更新理论，我们表明，在Cramér条件下，固定分布具有功率法尾巴。我们确定固定马尔可夫链的尾巴过程，证明点过程收敛和部分总和的收敛性。最初的动机来自Kesten，Kozlov和Spitzer Seninal 1975论文，该论文将随机环境模型中的随机步行连接到特殊的Galton-Watson过程，并在随机环境中移民。即使在这个非常特殊的环境中，我们也会获得新的结果。
We investigate subcritical Galton-Watson branching processes with immigration in a random environment. Using Goldie's implicit renewal theory we show that under general Cramér condition the stationary distribution has a power law tail. We determine the tail process of the stationary Markov chain, prove point process convergence, and convergence of the partial sums. The original motivation comes from Kesten, Kozlov and Spitzer seminal 1975 paper, which connects a random walk in a random environment model to a special Galton-Watson process with immigration in a random environment. We obtain new results even in this very special setting.
