本文针对有吸收点的一般 Q 过程，找到了新型 Doeblim 条件的充分条件并且推出了单生过程时该充分条件的显式表示.对于单死过程，我们找到了新型 Doeblin 条件的等价条件.之后应用不同于 Champagnat 和 Villemonais的论文[2的方法研究了带灾难的生灭过程。

本文分为四部分: 第一部分是引言.第二部分是一般 Q 过程、单生过程与新型 Doeblin 条件的充分条件.第三部分是单死过程与新型 Doeblin 条件的等价条件.第四部分是带灾难的生灭过程与新型 Doeblin 条件的等价条件。

The paper find a sufficient condition to new-type Doeblin condition for almost absorbed Q-processes .Then this condition can be explicitly represented for single birth processes .We find a condition equivalent to new-type Doeblin condition for single death processes. In the end we study one-dimensional birth and death processes with catastrophes in a different method from Champagnat and Villemonais.

The paper is divided into four parts. The first part is introduction and the second one is a sufficient condition to new-type Doeblin condition for Q-processes and single birth processes. Equivalent conditions to new-type Doeblin condition for single death processes are studied in the third part. And in the last part we study one-dimensional birth and death processes with catastrophes with the equivalent condition to new-type Doeblin condition.