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Zbl 1146.60058
Bakry, Dominique; Cattiaux, Patrick; Guillin, Arnaud
Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré. (English)
[J] J. Funct. Anal. 254, No. 3, 727-759 (2008). ISSN 0022-1236

Authors' 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.
[Gheorghe Oprişan (Bucureşti)]

MSC 2000:: *60J35 Transition functions
60J25 Markov processes with continuous parameter
60F25 Lp-limit theorems (probability)
31C25 Dirichlet spaces
11S99 Algebraic number theory over local and p-adic fields

Keywords: ergodic processes; Lyapunov functions; Poincaré inequalities; hypocoercivity

Cited in: Zbl 1186.26011

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