English

A large deviation inequality for vector functions on finite reversible Markov Chains

Probability 2009-09-29 v3 Statistics Theory Statistics Theory

Abstract

Let SNS_N 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 SNS_N 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.

Keywords

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)