Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 83, 2296-2333.
Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance
We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in 1-Wasserstein distance are also given. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processes.
Electron. J. Probab., Volume 16 (2011), paper no. 83, 2296-2333.
Accepted: 15 November 2011
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60B10: Convergence of probability measures
Secondary: 39B72: Systems of functional equations and inequalities
This work is licensed under aCreative Commons Attribution 3.0 License.
Boissard, Emmanuel. Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance. Electron. J. Probab. 16 (2011), paper no. 83, 2296--2333. doi:10.1214/EJP.v16-958. https://projecteuclid.org/euclid.ejp/1464820252