随机环境加权分枝过程的方差和Fuk-Nagaev型不等式

The Variance and Fuk-Nagaev Type Inequality for Weighted Branching Processes in a Random Environment

在对随机环境中加权分枝过程(Yn)的研究基础上,考虑其规范化过程Wn的方差及其收敛性,并予以了详细的证明,其中规范化过程为,是规范化序列,是随机环境分枝过程相关结论的拓展;并且建立了一个关于统计量的Fuk-Nagaev型不等式。

On the basis of the research on the weighted branching process (Yn) in random environments, the variance and convergence of its normalization process Wn are considered, and the de-tailed proof is provided. The normalization process is , and is the normalized se-quence, which is an extension of the conclusions related to the branching process in random envi-ronments. Besides, we establish a Fuk-Nagaev type inequality for .