The rest of the paper is divided two parts : the first part , which is composed of chapter 2 , chapter 3 and chapter 4 , is devoted to studying problems on the extended birth - death processes and / ^ - invariant distribution . the second part is contributed to studying problems on convergence properties , which is composed of chapter 5 , chapter 6 and chapter 7 . chapter 2 is devoted to studying an extended birth - death stable q - matrix with catastrophes 剩下的内容是本人在读博期间研究取得的主要结果,它们分为两部分:第一部分是广义生灭(拟) q -矩阵和马尔可夫q过程的不变测度,包括第二章、第三章和第四章;第二部分是序列的各种收敛性质,包括第五章、第六章和第七章。
Chapter 4 is dedicated to the study on - invariant distribution . first , as q - matrix is totally stable or uni - instantaneous , we prove the existence of - invariant distribution of q - function and identify the q - function . second , we generalize - invariant distribution to jump processes and obtain some good properties and results 第四章致力于-不变分布的研究,首先对q -矩阵为全稳定和单瞬时情形,证明了q -函数-不变分布的存在性,并且也把具体的q -函数构造出来了;然后把-不变分布推广到跳过程,得到了一些较好的性质和结果。