noone;A Note on Geometric Ergodicity of Markov Chains

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/65881

Title:	noone;A Note on Geometric Ergodicity of Markov Chains
Authors:	盧炤傑;Lu,Chao-Chieh
Contributors:	數學系
Keywords:	馬可夫鏈;幾何遍地性;收斂參數;Markov Chain;Geometric Ergodicity;Convergence parameter
Date:	2014-07-21
Issue Date:	2014-10-15 17:16:46 (UTC+8)
Publisher:	國立中央大學
Abstract:	對於可數多個態、同質的馬可夫鏈我們已經有一些基本的認知，而且由D. G. Kendall 證明一個對於數列 (p_ij^((n) )-π_ij) 幾何收斂的‘solidarty theorem’。我們想檢驗幾何遍地性以及去得到馬可夫鏈的幾何收斂參數 ρ_ij。因此，我們在中間建構並且推廣一些的馬可夫鏈的極限定理；此外，我們可以在一個共同的圓 C_(R^′ ) (R^′>R) 使生成函數P_00 (z)延拓成亞純函數(meromorphic function)使其在 z=R 有一個簡單極(simple pole)。最後，我們去推論出幾何遍地性以及幾何收斂參數 ρ_ij。;We already had known about some basic understanding of homogeneous Markov chain with countable state space, and D. G. Kendall has proved a ′solidarity theorem′ for geometric convergence of the sequences (p_ij^((n) )-π_ij ) with convergence parameter ρ_ij. We shall investigate the geometric ergodicity and the convergence parameters ρ_ij. Therefore, we construct and generate some theorems of Markov chain. Also, we extend the genereating function P_00 (z) as a meromorphic function within a common disk C_(R^′ ) (R^′>R) which it has only simple pole at z=R. Finally, we deduce some results for geometric ergodicity and convergence parameters ρ_ij.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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