Subgeometric ergodicity of strong Markov processes

We derive sufficient conditions for subgeometric f-ergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed return-time to a petite set. We then formulate a criterion for polynomial f-ergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R^n and storage models.Comment: Published at http://dx.doi.org/10.1214/105051605000000115 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org