|
|||||
|
|
Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré |
|
| Authors: | Dominique Bakry Patrick Cattiaux Arnaud Guillin |
| Institution: | a Laboratoire de Statistiques et Probabilités, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse cedex, France b Institut Universitaire de France, France c Ecole Polytechnique, CMAP, F-91128 Palaiseau cedex, France d Ecole Centrale Marseille et LATP, France e Université de Provence, Technopole Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille cedex 13, France |
| Abstract: | We study the relationship between two classical approaches for quantitative ergodic properties: the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of Poincaré type). We show that they can be linked through new inequalities (Lyapunov-Poincaré inequalities). Explicit examples for diffusion processes are studied, improving some results in the literature. The example of the kinetic Fokker-Planck equation recently studied by Hérau and Nier, Helffer and Nier, and Villani is in particular discussed in the final section. |
| Keywords: | Ergodic processes Lyapunov functions Poincaré inequalities Hypocoercivity |
| 本文献已被 ScienceDirect 等数据库收录！ | |