用隨機時間模擬馬可夫鏈

Abstract

本論文提供了一個模擬馬可夫鏈的方法，這方法可以避免大量計算，並且會提供一個完整的定理證明這個模擬方法是會收斂到馬可夫鏈的平衡分布。之後我們探討兩個特殊例子，討論當他不符合定理的前提，根據數值結果這方法不一定成立，最後提供了一個方法去修改這兩個例子讓他符合定理的前提假設。

In this thesis, we provided a simulated method, which can avoid lots of computations, to make the Markov chain approximate its stationary distribution and also gave a theorem to prove it. At first part, we gave a theorem to prove the convergence of new random variable. At second part, we gave two special cases of simulation and found the random variable will not converge to the stationary distribution if the chain does not satisfy the condition of theorem. At last, we gave a way to improve the chain.