Deeper Inside Finite-state Markov chains

Abstract

The eíĩective application o f Markov chains has been paid much attention, and it has raised a lot of thcoreticaỉ and applied problems. In this paper, vve vvould like to approach One of these problems vvhich is íìnding the long-run behavior of extremely huge-state Markov chains according to the direction of investigating the structure of Markov Graphto reduce complexity of computation. We focus on the vvay to access to the íìnite-state Markov chain theory via Graph theory.We suggested some basic knovvledge about State classiíìcation and a small project of modelling the structure and the moving process of the /inite-stateA íarkov Chain modeỉ.This project based on the remark that il is impossible to study deeperly the finite-state Markov Chain theory if we do not have the clear sense about the structure and the movement of it