# Stability of Markovian processes I: criteria for discrete-time Chains

@article{Meyn1992StabilityOM, title={Stability of Markovian processes I: criteria for discrete-time Chains}, author={Sean P. Meyn and Richard L. Tweedie}, journal={Advances in Applied Probability}, year={1992}, volume={24}, pages={542 - 574} }

In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the other. We show that these concepts of stability are largely equivalent for a major class of chains (chains with continuous components), or if the state space has a sufficiently rich class of appropriate sets (‘petite sets'). We use a discrete formulation of Dynkin's formula to establish unified…

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