Abstract
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 inhomoge-neous 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.
Original language | English |
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Pages (from-to) | 2126-2158 |
Number of pages | 33 |
Journal | Annals of Probability |
Volume | 36 |
Issue number | 6 |
DOIs | |
State | Published - 1 Nov 2008 |
Externally published | Yes |
Keywords
- Bounded martingale differences
- Concentration inequality
- Contracting markov chains
- Hidden markov chains
- Markov chains
- McDiarmid's bound
- Mixing coefficients
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty