博碩士論文 101221025 詳細資訊




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姓名 盧炤傑(Chao-Chieh Lu)  查詢紙本館藏   畢業系所 數學系
論文名稱 noone
(A Note on Geometric Ergodicity of Markov Chains)
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 馬可夫鏈
★ 幾何遍地性
★ 收斂參數
關鍵字(英) ★ Markov Chain
★ Geometric Ergodicity
★ Convergence parameter
論文目次 目錄 頁次
中文摘要 ................................................ i
英文摘要 ................................................ ii
謝誌  ................................................. iii
目錄  ................................................. iv
1 Introduction .................................. 1
2 Basic properties of Markov chains ............. 2
3 R-transient, R-recurrent and taboo probabilities
 ...................................................... 6
4 Limit properties of R-positive-recurrent  ...................................................... 14
5 Uniform geometric ergodicity for recurrent chains  ...................................................... 22
Appendix 1 ............................................ 28
Appendix 2 ............................................ 30
Appendix 3 ............................................ 31
References ............................................ 32

參考文獻 References
[1] D. Vere-Jones, Geometric ergodicity in denumerable Markov chains. Quarterly Journal of Mathematics (Oxford, Series 2, 1960), 13, 7-28.
[2] K. L. Chung, Markov Chains with Stationary Transition Probabilities (Berlin:1960)
[3] G. H. Hardy, Divergent Series (Oxford, 1949).
[4] C. Derman, ′A solution to a set of fundamental equations in Markov chains′, Proc. American Math. Soc. 5 (1954) 332-4.
[5] D. G. Kendall, ′Unitary dilations of Markov transition operators and the corresponding integral representations for transition-probability matrices′, in U. Grenander (ed.), Probability and statistics (Stockholm: Almqvist and Wiksell; New York, 1959).
[6] S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, ( 2nd ed. Academic Press, New York 1975).
指導教授 許順吉(Shuenn-Jyi Sheu) 審核日期 2014-7-21
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