The Annals of Probability
- Ann. Probab.
- Volume 36, Number 6 (2008), 2126-2158.
Concentration inequalities for dependent random variables via the martingale method
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.
Ann. Probab., Volume 36, Number 6 (2008), 2126-2158.
First available in Project Euclid: 19 December 2008
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Kontorovich, Leonid (Aryeh); Ramanan, Kavita. Concentration inequalities for dependent random variables via the martingale method. Ann. Probab. 36 (2008), no. 6, 2126--2158. doi:10.1214/07-AOP384. https://projecteuclid.org/euclid.aop/1229696598