中文摘要：

该文研究了变化环境中分枝过程的收敛定理.在环境分布不独立的情况下,给定环境分布的矩条件,证明了W_n依Lt收敛到W,并且W〉0,a.s.,以此为基础,给出了该过程Z_n的中心极限定理,以及logZ_n的重对数律.这些结果对研究其它的渐进性质以及偏差理论都有重要的意义.

英文摘要：

In this paper,we studied convergence theorems of the branching processes in varying environments.When the environment is not independence,at the moment conditions of the environment,we prove that W_nL_t→ W and W〉0,a.s.firstly,and then we give the central limit theorem of the process,at last we give the law of the iterated logarithm of log Z_n.Those results are very important to the other asymptotic properties and deviations of the process.