Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud

ESAIM: Probability and Statistics (2010)

  • Volume: 5, page 183-201
  • ISSN: 1292-8100

Abstract

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In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

How to cite

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Lezaud, Pascal. "Chernoff and Berry–Esséen inequalities for Markov processes." ESAIM: Probability and Statistics 5 (2010): 183-201. <http://eudml.org/doc/197777>.

@article{Lezaud2010,
abstract = { In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman. },
author = {Lezaud, Pascal},
journal = {ESAIM: Probability and Statistics},
keywords = {Markov process; Chernoff bound; Berry–Esséen; eigenvalues; perturbation theory.; Berry-Esséen; perturbation theory},
language = {eng},
month = {3},
pages = {183-201},
publisher = {EDP Sciences},
title = {Chernoff and Berry–Esséen inequalities for Markov processes},
url = {http://eudml.org/doc/197777},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Lezaud, Pascal
TI - Chernoff and Berry–Esséen inequalities for Markov processes
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 183
EP - 201
AB - In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.
LA - eng
KW - Markov process; Chernoff bound; Berry–Esséen; eigenvalues; perturbation theory.; Berry-Esséen; perturbation theory
UR - http://eudml.org/doc/197777
ER -

References

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