(The) simple space approach to the reversed absorbing markov chain

Abstract

We propose a new method of analyzing the reversed absorbing Markov chain. The results of the forward absorbing Markov chain are well-known. Most researches on the reversed absorbing Markov chain have been focused on finding the specific properties of it using respectively different techniques. In this thesis, we intend to find the method generally applicable and straghtforward. The reversed counterparts of some properties are intuitively derived. Then, we introduce the proper sample space method to find them. Its procedures are as follows : First, we properly define a sample space consisting of all the relevant variables having the property we intend to find. Then, we derive the joint, marginal and conditional probability distributions necessary for obtaining the property. Using this method, we can derive al the results obtained before and some new ones. Finally, we show that the proper sample space method can be adapted to obtain the results of the original forward chain. With the proposed method, we can find almost all the properties on the absorbing Markov chain.