Subgeometric Ergodicity of Strong Markov Processes

We derive sufficient conditions for subgeometric ƒ-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 ƒ-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.