Equilibria in stochastic economic models are often time series which fluctuate in complex ways. But it is sometimes possible to summarize the long run, average characteristics of these fluctuations. For example, if the law of motion determined by economic interactions in Markovian and if the equilibrium time series converges in a specific probabilistic sense then the long run behavior is completely determined by an invariant probability distribution. This paper develops and unifies a number of results found in the probability literature which enable one to prove, under very general conditions, the existence of an invariant distribution and the convergence of the corresponding Markov process.