本文考虑单死过程的一些数字特征的概率意义. 证明回返概率或灭绝概率数字特征的显示表示. 最后, 利用本文结果计算了两个例子的相关数字特征. 全文分为三部分:第一部分是引言, 预备知识和主要结果. 第二部分是单死过程中某些随机事件的概率计算. 第三部分生灭过程和分支过程的应用.

In the paper, we consider probabilistic meanings for some numerical characteristics of single death processes. At the same time, we prove extinction probability and returning probability, which are represented explicitly in terms of these numerical characteristics. In the end, two examples are also presented to illustrate the value of the results.The paper is divided into three parts. The first part includes background and preliminary data as well as main results. Some probabilities of events in single death processes are computed in the second part, and in the last part, we consider the application of birth-death processes and a generalized Markov branching process with these results.