The invariant distribution based on moment neuronal networks 基于矩神经网络下的不变分布
Invariant distribution is a greatly important property of standard transition function in continuous - time markov chains and jump processes , it is of considerably significnce to study it 不变分布是连续时间马氏链中标准转移函数及跳过程的一个重要性质,对不变分布的讨论有着十分重要的意义。
The dissertation is devoted to the studies on invariant distribution and convergence rate . the aims of the paper are to identify invariant distribution of q - function and to find criteria of convergence rate which are easy to check 本学位论文致力于不变分布和收敛速度的研究,其目的是得到q -函数不变分布的构造,以及容易验证的收敛速度判定准则。
The first part , which is composed of chapter 3 , chapter 4 , is devoted to studying problems on invariant distribution and - invariant distribution . the second part is contributed to studying problems on convergence rate , which is composed of chapter 5 , chapter 6 , chapter 7 剩下的内容分为两部分:第一部分讨论不变分布及-不变分布,包括第三章和第四章;第二部分研究收敛速度,包括第五章,第六章和第七章。
In chapter 3 , first we answer the open problem of williams ( 1979 ) . we solve the problem completely when q - matrix is totally stable or uni - instantaneous , that is , we not only prove the existence of q - function but also identify the q - function . second , for invariant distribution of jump processes , we also obtain some good results 第三章首先回答了williams ( 1979 )开问题,对q -矩阵为全稳定和单瞬时情形,完整的解决了该问题,也就是说,不仅证明了q -函数的存在性,而且还把具体的q -函数构造出来了;其次对跳过程的不变分布,也得到了很好的结果。
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。