A large deviation inequality for vector functions on finite reversible Markov Chains
Probability
2009-09-29 v3 Statistics Theory
Statistics Theory
Abstract
Let be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bernstein--Hoeffding inequality is derived for the probability of large deviations of and relates the probability to the spectral gap of the Markov chain. Examples suggest that this inequality is better than alternative inequalities if the chain has a sufficiently large spectral gap and the function is high-dimensional.
Cite
@article{arxiv.math/0508538,
title = {A large deviation inequality for vector functions on finite reversible Markov Chains},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:math/0508538},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/105051607000000078 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)