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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41260
標題: | 雙重擾動方法和馬可夫鏈 Double Perturbations to Markov Chains |
作者: | Han-Chiang Chen 陳漢強 |
指導教授: | 姜祖恕 |
關鍵字: | 擾動,雙重擾動,馬可夫鏈,指數衰退,邊界層, Perturbations,Double Perturbations,Markov Chains,Asymptotic Expansion,Exponential Decay,Boundary Layer,Asymptotic Validation, |
出版年 : | 2009 |
學位: | 碩士 |
摘要: | 這篇文章主要是利用雙重擾動方法去探討馬可夫鏈的行為。以往的文獻大多只有單一擾動,而這篇文章則是探討雙重擾動。本文會先建立數列,並說明所建立的數列收斂,最後舉例說明。而全文共分三章,第一章是引言與開頭,第二、三章則是本文主要探討的內容。其中,第二章會討論雙重擾動中,劇烈變化因子所代表的矩陣為不可分割的情況。第三章,則討論該矩陣能夠分割成數個子矩陣的情況。 This article focuses on double perturbations over Markov chains rather than singular perturbation, which has been discussed before. In this article, asymptotic expansion will be first constructed and then the remainder term will be shown to be controllable under some appropriate sense. Finally, some examples will be cited to illustrate what we want to investigate under the double perturbed model. This article can be divided into three chapters. The first chapter is introduction and preliminaries. The second chapter discusses the condition under which the fastest component of the double perturbations has only one class while the third chapter discusses this component has many classes. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41260 |
全文授權: | 有償授權 |
顯示於系所單位: | 數學系 |
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