關於連續時間有限馬可夫鏈的轉換機率矩陣

Abstract

關於連續時間馬可夫鏈的轉換機率矩陣之研究可分為兩個方面 , @為近似解法, 另一為精確解法,前者的概念主要將狀態轉換率加以齊一 ? (uniformization),並將連續時間予以離散化 (discretization),(Yoon nd Shanthikumar 總結了一些已提出的方法,並提出一些改良的方法,但在 瑤g論文中,所有方法都是近似解)後者則是藉著對Q (infinitesimal enerator matrix)作頻譜分解 (spectral decomposition),但隨著Q 結 c之不同,各種方法難易亦有別,本論文先復習三種重要的近似方法,給予 @些評論,之後,在近似解方面,則從最基本的方法出發,來和兩種重要的方 k作連貫,最後,我們舉一些可見的例子來比較各種方法(包括近似與精確 的優劣 There are two ways on the research of transition probability trices for continuous-time finite Markov Chains : Approximate d exact solution . The first employs the idea of uniformizing e transition rate and discretizing the time , (Yoon and Shan- ikunar reviewed several techniques which had been presented d proposed some modified techniques involving approximate lutions.) The second approach uses the concept of making spec- ral decomposition of Q (infinitesimal generator matrix) ,this proach involves deeply with the structure of Q.We review here ree important ways of approximation and make some comments on at , and then we will associate the presented ways of decomp- sition for exact solution with the very basic point of view. nally some examples are presented and various approaches ( cluding approximate and exact solutions ) are compared .