Tunneling and Metastability of Continuous Time Markov Chains

We propose a definition of tunneling and of metastability for a continuous time Markov process on countable state spaces. We obtain sufficient conditions for a irreducible positive recurrent Markov process to exhibit a tunneling behaviour. In the reversible case these conditions can be expressed in terms of the capacities and of the stationary measure of the Markov process. © 2010 Springer Science+Business Media, LLC.