Journal of Probability and Statistics
Volume 2013 (2013), Article ID 424601, 5 pages
http://dx.doi.org/10.1155/2013/424601
Research Article

On the Study of Transience and Recurrence of the Markov Chain Defined by Directed Weighted Circuits Associated with a Random Walk in Fixed Environment

Chrysoula Ganatsiou

Department of Civil Engineering, Section of Mathematics and Statistics, School of Technological Sciences, University of Thessaly, Pedion Areos, 38334 Volos, Greece

Received 23 October 2012; Revised 2 March 2013; Accepted 27 March 2013

Academic Editor: Man Lai Tang

Copyright © 2013 Chrysoula Ganatsiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the cycle representation theory of Markov processes, we investigate proper criterions regarding transience and recurrence of the corresponding Markov chain represented uniquely by directed cycles (especially by directed circuits) and weights of a random walk with jumps in a fixed environment.