CONCENTRATION INEQUALITIES FOR DEPENDENT RANDOM VARIABLES VIA THE MARTINGALE METHOD
成果类型：
Article
署名作者：
Kontorovich, Leonid (Aryeh); Ramanan, Kavita
署名单位：
Weizmann Institute of Science; Carnegie Mellon University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/07-AOP384
发表日期：
2008
页码：
2126-2158
关键词：
摘要：
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 oil 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 ail external 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.