TAILIEUCHUNG - Báo cáo " Deeper Inside Finite-state Markov chains "

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. | VNU Journal of Science Mathematics - Physics 23 2007 76-83 Deeper Inside Finite-state Markov chains Le Trung Kien1 Le Trung Hieu2 Tran Loc Hung1 Nguyen Duy Tien3 1 Department of Mathematics Hue University 77 Nguyen Hue Hue city Vietnam Mathematics Mechanics Faculty Saint-Petersburg State University Russia 3 Department of Mathematics Mechanics Informatics College of Science VNU 334 Nguyen Trai Hanoi Vietnam Received 8 December 2006 received in revised form 2 August 2007 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. Introduction It is undeniable that the finite-state Markov chain in recent years has lots of important applications in modelling the natural and social phenomena. We may enumerate some branches of science such as weather forecast system magement Web information searching machine learning which the model of finite-state Markov chain is applied for. Markov chain effective application has been paid much attention and it has raised a lot of theoretical problems as well as applied ones. One of these is that how to find the long-run behavior of Markov chain when the state space is extremely huge. For example to rank Webs based on the hyperlink structure of Web Graph PageRank .

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