Metastable distributions of Markov chains with rare transitions
  In this paper we consider Markov chains with transition rates that depend on a small parameter $\varepsilon$. Under a mild assumption on the asymptotics of these transition rates, we describe the behavior of the chain at various $\varepsilon$-dependent time scales, i.e., we calculate the metastable distributions. 
Mark Freidlin, Leonid Koralov
math.PR