一個在馬可夫鏈上的穩定問題

Abstract

在周和吳之前的研究中，他們使用V ar(T)/(E(T))2 來衡量一個吸 收態的馬可夫鏈。在沒有任何限制的情況下，他們已經證明出最穩定 的馬可夫鏈是單方向的馬可夫鏈。然後想在對稱的情況下找尋最穩定 的馬可夫鏈，而這兩位老師猜測也會有類似的結果。在這篇論文中， 我證明出當狀態數小於4 的時候，他們的猜測是正確的。

In Chow and Wu [1], they used V ar(T)/(E(T))2 to measure the stability of an absorbing Markov Chain where T is the absorbing time. Without any restriction, they proved that the most stable absorbing Markov Chain is the one way chains. Furthermore, they add some restriction on the Markov chain and discuss the problem on symmetric Markov chains. In this thesis, the conjecture for n 3 is verified where n is the number of state space when the initial state is determined.