带拯救的碰撞分枝过程的常返性与遍历性

Recurrence and Ergodicity Properties of the Collision Branching Processes with Resurrection

考虑了一类带有拯救的碰撞分枝过程,给出了过程的正则性与唯一性准则,并得到了常返性和遍历性的充要条件.同时,给出了指数遍历性的一个便于验证的充分条件.

This paper considers the collision branching processes with resurrection. The regularity and uniqueness criterion for such processes are presented. The recurrence and ergodicity properties are also considered. Moreover, the recurrence, ergodicity and strongly ergodicity criteria for such processes are established. A sufficient condition for such processes to be exponentially ergodic is given.