论文标题
在随机环境中的Galton-Watson过程的一个明确解决的模型
One Explicitly Solvable Model For The Galton-Watson Processes In the Random Environment
论文作者
论文摘要
在本文中，我们研究了随机环境中的Galton-Watson过程，当时每一代的后代数量具有随机参数的分数线性生成函数。在这种情况下，可以明确计算$ n_t $的分布，当时$ t = 0,1,2，\ cdots $当时的粒子数。我们介绍了此类过程的分类，并限制了两种类型的定理：淬火类型，该类型是用于随机环境和退火类型的固定实现，其中包括环境上的平均值。
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the distribution of $N_t$, the number of particles at the moment time $t=0,1,2,\cdots$ can be calculated explicitly. We present the classification of such processes and limit theorems of two types: quenched type which is for the fixed realization of the random environment and annealed type which includes the averaging over the environment.
