On the Study of Circuit Chains Associated with a Random Walk with Jumps in Fixed, Random Environments: Criteria of Recurrence and Transience

Abstract

By considering a nonhomogeneous random walk with jumps (with steps − 1 or +1 or in the same position having a right-elastic barrier at 0) we investigate the unique representations by directed circuits and weights of the corresponding Markov chains (circuit chains) in fixed, random environments. This will give us the possibility to find suitable criteria regarding the properties of recurrence and transience of the above-mentioned circuit chains in fixed, random environments.