deviation bounds for additive functionals of markov processes

Patrick Cattiaux; Arnaud Guillin

ESAIM: Probability and Statistics (2007)

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

Abstract

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In this paper we derive non asymptotic deviation bounds for ℙ 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 (2007): 12-29. <http://eudml.org/doc/104392>.

@article{Cattiaux2007,
abstract = { In this paper we derive non asymptotic deviation bounds for $$\{\mathbb P\}\_\nu (|\frac 1t \int\_0^t V(X\_s) \{\rm d\}s - \int V \{\rm d\} \mu | \geq R)$$ 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.). },
author = {Cattiaux, Patrick, Guillin, Arnaud},
journal = {ESAIM: Probability and Statistics},
keywords = {Deviation inequalities; functional inequalities; additive functionals.; deviation inequalities; additive functionals},
language = {eng},
month = {11},
pages = {12-29},
publisher = {EDP Sciences},
title = {deviation bounds for additive functionals of markov processes},
url = {http://eudml.org/doc/104392},
volume = {12},
year = {2007},
}

TY - JOUR
AU - Cattiaux, Patrick
AU - Guillin, Arnaud
TI - deviation bounds for additive functionals of markov processes
JO - ESAIM: Probability and Statistics
DA - 2007/11//
PB - EDP Sciences
VL - 12
SP - 12
EP - 29
AB - In this paper we derive non asymptotic deviation bounds for $${\mathbb P}_\nu (|\frac 1t \int_0^t V(X_s) {\rm d}s - \int V {\rm d} \mu | \geq R)$$ 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.).
LA - eng
KW - Deviation inequalities; functional inequalities; additive functionals.; deviation inequalities; additive functionals
UR - http://eudml.org/doc/104392
ER -

References

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