Open Access
November 2008 Concentration inequalities for dependent random variables via the martingale method
Leonid (Aryeh) Kontorovich, Kavita Ramanan
Ann. Probab. 36(6): 2126-2158 (November 2008). DOI: 10.1214/07-AOP384


The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous Markov chains and hidden Markov chains, and an extremal property associated with their martingale difference bounds is established. This work complements and generalizes certain concentration inequalities obtained by Marton and Samson, while also providing different proofs of some known results.


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Leonid (Aryeh) Kontorovich. Kavita Ramanan. "Concentration inequalities for dependent random variables via the martingale method." Ann. Probab. 36 (6) 2126 - 2158, November 2008.


Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1154.60310
MathSciNet: MR2478678
Digital Object Identifier: 10.1214/07-AOP384

Primary: 60E15
Secondary: 60G42 , 60J10

Keywords: bounded martingale differences , concentration inequality , contracting Markov chains , hidden Markov chains , Markov chains , McDiarmid’s bound , mixing coefficients

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 6 • November 2008
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