SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES

By Gersende Fort, Gareth O. Roberts. 2005

104 citations recorded by the source corpus.

We derive sufficient conditions for subgeometricf-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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dcca1151e0f405d30a6ec4b763d9fe0a45dc67fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, background): “Note that once again, results of [12, 9] would give, via Theorem 2.”
Subgeometric rates of convergence of Markov processes in the Wasserstein metric (2012, methodology): “However, note that we cannot apply this proposition directly because in contrast to Fort and Roberts, we assumed neither that the set {V (x) ≤ R} is petite nor that the process X is Harris-recurrent with invariant measure.”
Characterizations of Overtaking Optimality for Controlled Diffusion Processes (2008, unknown): “Assumption 2.2 can be used in the context of general Markov processes (as in [ 9 , 15, 30]) or in the special case of diffusions (as in [1, 4, 12, 14, 19, 24]).”
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “It should be mentioned that subgeometric ergodicity of Markov processes has been studied by many others authors in various settings; see [8, 17, 24, 34, 43, 50, 58, 59] and the references therein.”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, methodology): “By combining the results of the LD-condition argument and general stability theory for Markov processes, it is possible to formulate subexponential- and polynomial-ergodicity versions, as well as the ergodicity version (without rate specification); see, for example, Meyn and Tweedie [34] and Fort an”
Lyapunov conditions for Super Poincaré inequalities (2009, unknown): “[16, 18, 15]).”