ROSENTHAL-TYPE INEQUALITIES FOR THE MAXIMUM OF PARTIAL SUMS OF STATIONARY PROCESSES AND EXAMPLES

• 成果类型: Article
• 署名作者: Merlevede, Florence; Peligrad, Magda
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP694
• 发表日期: 2013
• 页码: 914-960
• 关键词: CENTRAL-LIMIT-THEOREM; invariance-principle; STRONG LAW; SEQUENCES; moment; CONVERGENCE; rates

摘要

The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob maximal inequality for martingales and dyadic induction. Various applications are also provided.