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 · Journal of Probability and Statistics · 2013
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.