Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud

ESAIM: Probability and Statistics (2001)

  • 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 (2001): 183-201. <http://eudml.org/doc/104272>.

@article{Lezaud2001,
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},
language = {eng},
pages = {183-201},
publisher = {EDP-Sciences},
title = {Chernoff and Berry–Esséen inequalities for Markov processes},
url = {http://eudml.org/doc/104272},
volume = {5},
year = {2001},
}

TY - JOUR
AU - Lezaud, Pascal
TI - Chernoff and Berry–Esséen inequalities for Markov processes
JO - ESAIM: Probability and Statistics
PY - 2001
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
UR - http://eudml.org/doc/104272
ER -

References

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Citations in EuDML Documents

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  1. Eva Löcherbach, Dasha Loukianova, Polynomial deviation bounds for recurrent Harris processes having general state space
  2. Patrick Cattiaux, Arnaud Guillin, Deviation bounds for additive functionals of Markov processes
  3. Patrick Cattiaux, Arnaud Guillin, deviation bounds for additive functionals of markov processes
  4. Eva Löcherbach, Dasha Loukianova, Oleg Loukianov, Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times
  5. Déborah Ferré, Loïc Hervé, James Ledoux, Limit theorems for stationary Markov processes with L2-spectral gap

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