Deviation bounds for additive functionals of Markov processes

Patrick Cattiaux; Arnaud Guillin

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 12-29
  • ISSN: 1292-8100

Abstract

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In this paper we derive non asymptotic deviation bounds for ν ( | 1 t ∫ 0 t V ( X s ) d s - ∫ V d μ | ≥ R ) where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V , and various regularity assumptions for μ . Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).

How to cite

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Cattiaux, Patrick, and Guillin, Arnaud. "Deviation bounds for additive functionals of Markov processes." ESAIM: Probability and Statistics 12 (2008): 12-29. <http://eudml.org/doc/245164>.

@article{Cattiaux2008,
abstract = {In this paper we derive non asymptotic deviation bounds for\[¶\_\nu (|\frac\{1\}\{t\} \int \_0^t V(X\_s) \{\rm d\}s - \int V \{\rm d\} \mu | \ge R)\]where $X$ is a $\mu $ stationary and ergodic Markov process and $V$ is some $\mu $ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\mu $. Regularity means here that $\mu $ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).},
author = {Cattiaux, Patrick, Guillin, Arnaud},
journal = {ESAIM: Probability and Statistics},
keywords = {deviation inequalities; functional inequalities; additive functionals},
language = {eng},
pages = {12-29},
publisher = {EDP-Sciences},
title = {Deviation bounds for additive functionals of Markov processes},
url = {http://eudml.org/doc/245164},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Cattiaux, Patrick
AU - Guillin, Arnaud
TI - Deviation bounds for additive functionals of Markov processes
JO - ESAIM: Probability and Statistics
PY - 2008
PB - EDP-Sciences
VL - 12
SP - 12
EP - 29
AB - In this paper we derive non asymptotic deviation bounds for\[¶_\nu (|\frac{1}{t} \int _0^t V(X_s) {\rm d}s - \int V {\rm d} \mu | \ge R)\]where $X$ is a $\mu $ stationary and ergodic Markov process and $V$ is some $\mu $ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\mu $. Regularity means here that $\mu $ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).
LA - eng
KW - deviation inequalities; functional inequalities; additive functionals
UR - http://eudml.org/doc/245164
ER -

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Citations in EuDML Documents

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  1. Patrick Cattiaux, Mawaki Manou-Abi, Limit theorems for some functionals with heavy tails of a discrete time Markov chain
  2. Patrick Cattiaux, Arnaud Guillin, Trends to equilibrium in total variation distance
  3. Eva Löcherbach, Oleg Loukianov, Dasha Loukianova, Spectral condition, hitting times and Nash inequality
  4. Eva Löcherbach, Dasha Loukianova, Polynomial deviation bounds for recurrent Harris processes having general state space
  5. Patrick Cattiaux, Arnaud Guillin, Pierre André Zitt, Poincaré inequalities and hitting times
  6. Eva Löcherbach, Dasha Loukianova, Oleg Loukianov, Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times

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