The invariant distribution based on moment neuronal networks 基于矩神經(jīng)網(wǎng)絡(luò)下的不變分布
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 不變分布是連續(xù)時間馬氏鏈中標準轉(zhuǎn)移函數(shù)及跳過程的一個重要性質(zhì),對不變分布的討論有著十分重要的意義。
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 本學位論文致力于不變分布和收斂速度的研究,其目的是得到q -函數(shù)不變分布的構(gòu)造,以及容易驗證的收斂速度判定準則。
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 剩下的內(nèi)容分為兩部分:第一部分討論不變分布及-不變分布,包括第三章和第四章;第二部分研究收斂速度,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 )開問題,對q -矩陣為全穩(wěn)定和單瞬時情形,完整的解決了該問題,也就是說,不僅證明了q -函數(shù)的存在性,而且還把具體的q -函數(shù)構(gòu)造出來了;其次對跳過程的不變分布,也得到了很好的結(jié)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 剩下的內(nèi)容是本人在讀博期間研究取得的主要結(jié)果,它們分為兩部分:第一部分是廣義生滅(擬) q -矩陣和馬爾可夫q過程的不變測度,包括第二章、第三章和第四章;第二部分是序列的各種收斂性質(zhì),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-不變分布的研究,首先對q -矩陣為全穩(wěn)定和單瞬時情形,證明了q -函數(shù)-不變分布的存在性,并且也把具體的q -函數(shù)構(gòu)造出來了;然后把-不變分布推廣到跳過程,得到了一些較好的性質(zhì)和結(jié)果。