Deeper Inside Finite-state Markov chains

Abstract. The effective application of Markov chains has been paid much attention, and it has raised a lot of theoretical and applied problems. In this paper, we would like to approach one of these problems which is finding the long-run behavior of extremely huge-state Markov chains according to the direction of investigating the structure of Markov Graph to reduce complexity of computation. We focus on the way to access to the finite-state Markov chain theory via Graph theory. We suggested some basic knowledge about state classification and a small project of modelling the structure and the moving process of the finite-state Markov chain model. This project based on the remark that it 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. 1