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2013 Measure concentration through non-Lipschitz observables and functional inequalities
Aldéric Joulin, Arnaud Guillin
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Electron. J. Probab. 18: 1-26 (2013). DOI: 10.1214/EJP.v18-2425


Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and offers an unified treatment of diffusions and pure-jump Markov processes on unbounded spaces.


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Aldéric Joulin. Arnaud Guillin. "Measure concentration through non-Lipschitz observables and functional inequalities." Electron. J. Probab. 18 1 - 26, 2013.


Accepted: 24 June 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1282.60024
MathSciNet: MR3078024
Digital Object Identifier: 10.1214/EJP.v18-2425

Primary: 46E35
Secondary: 60E15 , 60J27 , 60J60 , 60K35

Keywords: Concentration , diffusion process , functional inequality , invariant measure , jump process , Lyapunov condition , reversible Markov process

Vol.18 • 2013
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