有限馬可夫鏈和半馬可夫鏈的弱結合性

Abstract

考慮一個不能刪減且齊次的有限狀態之馬可夫鏈,我們感興趣的是相對於 這一個狀態空間的分割,一個由原來過程所產生的結合過程是否仍然為一 個齊次的馬可夫鏈.在一個溫和的情況下,關於弱結合性的充分必要條件及 一些具有結合性的初始向量的集合特性可被獲得.更進一步的,我們發現半 馬可夫過程也擁有類似馬可夫鏈的一些結合性及弱結合性的性質. Consider an irreducible and homogeneous Markov chain withinite state space. We are interested to know whether the lumped process constructed from the original one with respect to a given partition of its state space is still a homogeneous Markov chain. Under a mild condition, a necessary and sufficient condition foreak lumpability, and the characterzation of the set of initialarting vectors which make it lumpable are obtained.thermore, we find that semi-Markov processes own someability and weak lumpability properties similar to those Markov chains.