带移民的单生过程

Single Birth Processes with Immigration

本文给出了带移民单生过程唯一性、常返性、遍历、强遍历的显式判别准则和指数遍历的显式充分条件,以及0点首中时的n阶矩显式表达式.作为应用,给出了带移民生灭过程的相关性质,并且在文末讨论了几个例子的各种遍历性.

In this paper, the explicit criteria for uniqueness, recurrence, ergodicity, strong ergodicity of the single birth processes with immigration are presented. Mean- while, an explicit sufficient condition for exponential ergodicity of the processes is obtained. In addition, the explicit expressions on the polynomial moments of the first hitting time are also founded. As an application, some properties are obtained on the birth death processes with immigration. Some examples are illustrated at the end.