Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 65, 26 pp.
Measure concentration through non-Lipschitz observables and functional inequalities
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.
Electron. J. Probab., Volume 18 (2013), paper no. 65, 26 pp.
Accepted: 24 June 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
This work is licensed under a Creative Commons Attribution 3.0 License.
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