We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a “positive curvature” assumption expressing a kind of metric ergodicity, which generalizes the Ricci curvature from differential geometry and, on finite graphs, amounts to contraction under path coupling.
Publié le : 2010-11-15
Classification:
Markov chain Monte Carlo,
concentration of measure,
Ricci curvature,
Wasserstein distance,
65C05,
60J22,
62E17
@article{1285334210,
author = {Joulin, Ald\'eric and Ollivier, Yann},
title = {Curvature, concentration and error estimates for Markov chain Monte Carlo},
journal = {Ann. Probab.},
volume = {38},
number = {1},
year = {2010},
pages = { 2418-2442},
language = {en},
url = {http://dml.mathdoc.fr/item/1285334210}
}
Joulin, Aldéric; Ollivier, Yann. Curvature, concentration and error estimates for Markov chain Monte Carlo. Ann. Probab., Tome 38 (2010) no. 1, pp. 2418-2442. http://gdmltest.u-ga.fr/item/1285334210/