Locally contracting iterated functions and stability of Markov chains

We consider Markov chains in the context of iterated random functions and s how the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift condition, extending results o f Diaconis and Freedman. From these we deduce various other topological sta bility properties of the chains. Our conditions are typically satisfied by, for example, queueing and storage models where the global Lipschitz condit ion used by Diaconis and Freedman normally fails.