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

被引：22

作者：

Merlevede, Florence ^{[1
,2
]}

Peligrad, Magda ^{[3
]}

机构：

[1] Univ Paris Est Marne La Vallee, LAMA, F-77454 Marne La Vallee, France

[2] Univ Paris Est Marne La Vallee, UMR CNRS 8050, F-77454 Marne La Vallee, France

[3] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

ANNALS OF PROBABILITY | 2013年 / 41卷 / 02期

关键词：

Moment inequality; maximal inequality; Rosenthal inequality; stationary sequences; martingale; projective conditions; CENTRAL-LIMIT-THEOREM; INVARIANCE-PRINCIPLE; STRONG LAW; SEQUENCES; MOMENT; CONVERGENCE; RATES;

D O I：

10.1214/11-AOP694

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：914 / 960

页数：47

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