Chrysoula Ganatsiou

Following the context of the theory of *cycle-circuit representations of Markov processes*, regarding the representations of Markov processes as decompositions in terms of the circuit passage functions, we attempt to investigate unique representations by directed circuits and weights for random walks with jumps in fixed, random environments, that is, to provide proper unique Markov chains' circuit representations of these random walks in ergodic fixed, random environments. This will give us the possibility to study the criterions regarding the properties of recurrence or transience of the corresponding Markov chain, the *circuit chain*.

**References:**

1. S. Kalpazidou, *Cycle Representations of Markov Processes*, Springer-Verlag, New York, 1995.

2. S. Kalpazidou, Ch. Ganatsiou, On the inversion of multiple Markov chains, *Far East Journal of Mathematical Sciences*, **10**, 1, 1-13(2003)

3. J. MacQueen, Circuit Processes, *Ann. Probab.*, 9, 604-610, 1981.

**Keywords:** cycle representations; random walk; circuits and weights; fixed, random environment

**Biography:** Dr. of Mathematics and Statistics

University of Thessaly

Department of Civil Engineering

School of Technological Sciences

Section of Mathematics and Statistics

Pedion Areos, 38334, Volos, Greece