非齊次馬可夫鏈之轉置機率

Abstract

本篇論文是從一與時間相關的微矩陣的觀點來考慮非齊次馬可夫鏈。在一些不同的條件下，我們可以找到轉置機率精確解的形式，但針對一般形式的非齊次馬可夫鏈，我們可以找到一些較有效率的逼近方式來逼近轉置機率。同時，在本論文中，亦列舉幾個不同的例子和數值結果加以說明。

Consider a nonhomogeneous Markov chain with some time dependent infinitesimal matrix. The exact transition probabilities under various conditions are obtained. For general nonhomogeneous Markov chains with continuous infinitesimal matrices, we find an efficient way to approximate transition probabilities. Various examples and some numerical results are also presented.