本文分为六个部分.第一章综述.第二章给出有限态吸收生灭过程的击中时分布.第三章研究过程非唯一条件下最小过程的击中时分布.第四章给出正则边界下最大生灭过程的击中时和最快强平稳时分布.第五章研究过程非唯一条件下生灭过程的逼近问题.这些结论在过程唯一时一般不成立.第六章研究过程非唯一条件下遍历单生过程的逼近问题.

This thesis consists of sixes chapters. The first chapter is the summary. In the second chapter, we give the hitting time distributions for finite absorbing birth and death processes. In the third chapter, we study hitting time distributions for the minimal birth and death process when the processes are not unique. In the fourth chapter, we obtain distributions of the hitting times and the fastest strong stationary time for the ``maximal'' birth and death process. In the fifth chapter, we investigate the approximation for the birth and death process when processes are not unique. In the sixth chapter, we study the approximation for ergodic single birth processes when processes are not unique.