带拯救的两参数Markov碰撞过程的遍历性

Ergodicity properties of 2-parameter Markov collision processes with resurrection

本文考虑了一类带拯救的两参数Markov碰撞过程.首先讨论了带拯救的两参数Markov碰撞q-矩阵发生函数的性质,通过发生函数给出了过程的正则性和唯一性判别准则,得到了过程的常返性和遍历性的充分必要条件,并给出了几个易于验证的充分条件.最后,给出了遍历情形下该过程平稳分布的发生函数,并给出了过程强遍历的判别准则.

This paper concentrates on investigating ergodicity properties of 2-parameter Markov collision pro- cesses with resurrection. In this paper, some properties of the generating functions for 2-parameter Markov collision q-matrix with resurrection are firstly investigated in detail. By using the generating functions of the corresponding q-matrix, the criteria for regularity and uniqueness for such structure are first established. Easy checking criteria including several clear-cut corollaries are established for recurrence and ergodicity of such pro- cesses. Finally, the equilibrium distribution is given in an elegant closed form for the ergodic case. The criteria for strongly ergodicity is also given.