Electronic Journal of Probability

Measure concentration through non-Lipschitz observables and functional inequalities

Aldéric Joulin and Arnaud Guillin

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 65, 26 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064290

Digital Object Identifier
doi:10.1214/EJP.v18-2425

Mathematical Reviews number (MathSciNet)
MR3078024

Zentralblatt MATH identifier
1282.60024

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 60E15: Inequalities; stochastic orderings 60J27: Continuous-time Markov processes on discrete state spaces 60J60: Diffusion processes [See also 58J65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Joulin, Aldéric; Guillin, Arnaud. Measure concentration through non-Lipschitz observables and functional inequalities. Electron. J. Probab. 18 (2013), paper no. 65, 26 pp. doi:10.1214/EJP.v18-2425. https://projecteuclid.org/euclid.ejp/1465064290


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