We consider the regularity and ergodic properties of the Branching Collision Process with Immigration (BCIP) in this paper. We establish an easy checking sufficient condition under which the Feller minimal BCIP is honest. We provide some good conditions under which the Feller minimal BCIP is positive recurrent and then establish an analytic form of the generating function of the stationary distribution. The closely associated expected hitting times are also considered. Examples and numerical calculations are provided to illustrate our results.

中文翻译：

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迁移过程中的分支冲突过程

在本文中，我们考虑了带有移民的分支碰撞过程（BCIP）的规则性和遍历性。我们建立了容易检查的充分条件，在此条件下Feller最低BCIP诚实。我们提供了一些条件，在这些条件下，费勒最小BCIP为正递归，然后建立平稳分布的生成函数的解析形式。还考虑了紧密相关的预期击球时间。提供了示例和数值计算来说明我们的结果。