Open Access
VOL. 9 | 2013 A counterexample concerning the extension of uniform strong laws to ergodic processes
Terrence Adams, Andrew Nobel

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

Inst. Math. Stat. (IMS) Collect., 2013: 1-4 (2013) DOI: 10.1214/12-IMSCOLL901


We present a construction showing that a class of sets $\mathcal{C}$ that is Glivenko-Cantelli for an i.i.d. process need not be Glivenko-Cantelli for every stationary ergodic process with the same one dimensional marginal distribution. This result provides a counterpoint to recent work extending uniform strong laws to ergodic processes, and a recent characterization of universal Glivenko Cantelli classes.


Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1321.60053
MathSciNet: MR3186744

Digital Object Identifier: 10.1214/12-IMSCOLL901

Primary: 60F15
Secondary: 60G10

Keywords: cutting and stacking , ergodic process , Glivenko-Cantelli , uniform laws of large numbers

Rights: Copyright © 2010, Institute of Mathematical Statistics

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