Tightness for Non-irreducible Markov Chains
P. W. Glynn and S. Meyn
Technical Report, Department of Engineering-Economic Systems and Operations Research, Stanford University, (1997)
In this paper we develop Foster-type criteria guaranteeing tightness for Markov chains which are not necessarily irreducible. The results include criteria for both tightness of the marginal distributions and tightness of the Cesaro-averaged transition probabilities. In addition, we obtain results guaranteeing boundedness in expectation for real-valued functionals of the chain.