Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré

@article{Bakry2007RateOC,
  title={Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincar{\'e}},
  author={Dominique Bakry and Patrick Cattiaux and Arnaud Guillin},
  journal={Journal of Functional Analysis},
  year={2007},
  volume={254},
  pages={727-759}
}
On the Lyapunov Foster Criterion and Poincaré Inequality for Reversible Markov Chains
This article presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster–Lyapunov drift condition. Besides its relative simplicity, there
Poincaré inequalities and hitting times
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible
POINCARÉ TYPE INEQUALITIES FOR A DEGENERATE PURE JUMP MARKOV PROCESS
We study Talagrand concentration and Poincaré type inequalities for unbounded pure jump Markov processes. In particular we focus on processes with degenerate jumps that depend on the past of the
E INEQUALITIES AND HITTING TIMES
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible
Concentration and Poincar\'e type inequalities for a degenerate pure jump Markov process.
We study Talagrand concentration and Poincar\'e type inequalities for unbounded pure jump Markov processes. In particular we focus on processes with degenerate jumps that depend on the past of the
Wasserstein contraction and Poincar\'e inequalities for elliptic diffusions at high temperature
We consider elliptic diffusion processes on Rd. Assuming that the drift contracts distances outside a compact set, we prove that, at a sufficiently high temperature, the Markov semi-group associated
Central limit theorems for additive functionals of ergodic Markov diffusions processes
We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as
Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases
Abstract We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the confining
...
...