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

被引：158
作者：
Bakry, Dorninique [1 ]
Cattiaux, Patrick [1 ,2 ]
Guillin, Arnaud [3 ,4 ,5 ]
机构：
[1] Univ Toulouse 3, Lab Stat & Probabil, F-31062 Toulouse, France
[2] Ecole Polytech, CMAP, F-91128 Palaiseau, France
[3] Ecole Cent Marseille, Marseille, France
[4] LATP, Marseille, France
[5] Univ Aix Marseille 1, F-13453 Marseille 13, France
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2008年 / 254卷 / 03期
关键词：
ergodic processes; Lyapunov functions; Poincare inequalities; hypocoercivity;
D O I：
10.1016/j.jfa.2007.11.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Poincare type). We show that they can be linked through new inequalities (Lyapunov-Poincare 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 Herau and Nier, Helffer and Nier, and Villani is in particular discussed in the final section. (C) 2007 Elsevier Inc. All rights reserved.
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收藏
页码：727 / 759
页数：33
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