A Glivenko-Cantelli Theorem for almost additive functions
Probability
2018-09-28 v1 Statistics Theory
Statistics Theory
Abstract
We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~. Under certain conditions on the random sequence, short range correlations are allowed as well. We have an explicit error estimate, consisting of a probabilistic and a geometric part. We apply the results to yield uniform convergence for several quantities arising naturally in statistical physics.
Cite
@article{arxiv.1606.07664,
title = {A Glivenko-Cantelli Theorem for almost additive functions},
author = {Christoph Schumacher and Fabian Schwarzenberger and Ivan Veselic},
journal= {arXiv preprint arXiv:1606.07664},
year = {2018}
}
Comments
31 pages, to appear in Stochastic Processes and Applications