# 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} }

## 113 Citations

### On the Lyapunov Foster Criterion and Poincaré Inequality for Reversible Markov Chains

- MathematicsIEEE Transactions on Automatic Control
- 2022

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…

### Hypoelliptic entropy dissipation for stochastic differential equations

- Mathematics
- 2021

. We study the Lyapunov convergence analysis for degenerate and non-reversible stochastic diﬀerential equations (SDEs). We apply the Lyapunov method to the Fokker-Planck equation, in which the…

### POINCARÉ TYPE INEQUALITIES FOR A DEGENERATE PURE JUMP MARKOV PROCESS

- Mathematics
- 2018

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

- Mathematics
- 2010

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…

### Poincare inequality and exponential integrability of the hitting times of a Markov process

- Mathematics
- 2013

Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a…

### Concentration and Poincar\'e type inequalities for a degenerate pure jump Markov process.

- Mathematics
- 2019

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

- Mathematics
- 2022

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

- Mathematics
- 2011

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…