Concentration inequalities for dependent Random variables via the martingale method

Details Concentration inequalities for dependent Random variables via the martingale method Concentration inequalities for dependent Random variables via the martingale method

2006-09-29

arxiv.org/abs/math/0609835v2

Annals of Probability 2008, Vol. 36, No. 6, 2126-2158

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP384 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

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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