Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2013, Article ID 424601, 5 pages
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

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.

Linked References

  1. S. Kalpazidou, Cycle Representations of Markov Processes, Springer, New York, NY, USA, 1995.
  2. J. MacQueen, “Circuit processes,” Annals of Probability, vol. 9, pp. 604–610, 1981. View at Publisher · View at Google Scholar
  3. Q. Minping and Q. Min, “Circulation for recurrent markov chains,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 59, no. 2, pp. 203–210, 1982. View at Publisher · View at Google Scholar · View at Scopus
  4. A. H. Zemanian, Infinite Electrical Networks, Cambridge University Press, Cambridge, UK, 1991.
  5. Yv. Derriennic, “Random walks with jumps in random environments (examples of cycle and weight representations),” in Probability Theory and Mathematical Statistics: Proceedings of The 7th Vilnius Conference 1998, B. Grigelionis, J. Kubilius, V. Paulauskas, V. A. Statulevicius, and H. Pragarauskas, Eds., pp. 199–212, VSP, Vilnius, Lithuania, 1999. View at Google Scholar
  6. S. Karlin and H. Taylor, A First Course in Stochastic Processes, Academic Press, New York, NY, USA, 1975.