EXPONENTIAL INEQUALITIES FOR SELF-NORMALIZED MARTINGALES WITH APPLICATIONS

• 成果类型: Article
• 署名作者: Bercu, Bernard; Touati, Abderrahmen
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Inria; CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux; Universite de Carthage
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP506
• 发表日期: 2008
• 页码: 1848-1869
• 关键词: large deviation rates; bounds

摘要

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.