On the study of transience and recurrence of the markov chain defined by directed weighted circuits associated with a random walk in fixed environment

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. © 2013 Chrysoula Ganatsiou.