A new maximal inequality and invariance principle for stationary sequences

• 成果类型: Article
• 署名作者: Peligrad, M; Utev, S
• 署名单位: University System of Ohio; University of Cincinnati; University of Nottingham
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000001035
• 发表日期: 2005
• 页码: 798-815
• 关键词: CENTRAL-LIMIT-THEOREM; mixing sequences; random-variables; markov-chains

摘要

We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713-724]. Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.