Study of almost everywhere convergence of series by mean of martingale methods

被引：4

作者：

Cuny, Christophe ^{[1
]}

Fan, Ai Hua ^{[2
]}

机构：

[1] Ecole Cent Paris, Lab MAS, F-92295 Chatenay Malabry, France

[2] Univ Picardie Jules Verne, LAMFA UMR 7352, CNRS, 33 Rue St Leu, F-80039 Amiens 1, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2017年 / 127卷 / 08期

关键词：

Ergodic series; Dilated series; Martingale; Transfer operator; LACUNARY TRIGONOMETRIC SERIES; STRONG INVARIANCE-PRINCIPLES; DEPENDENT RANDOM-VARIABLES; CENTRAL LIMIT-THEOREMS; RIESZ PRODUCTS; STATIONARY-PROCESSES; MAXIMAL INEQUALITY; DILATED FUNCTIONS; SURE CONVERGENCE; ERGODIC-THEORY;

D O I：

10.1016/j.spa.2016.12.006

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：

Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan (2015), and to dilated series, including Davenport series, which completes results of Gaposhkin (1967) (see also Gaposhkin (1968)). Applications are also given to the almost everywhere convergence with respect to Riesz products of lacunary series. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：2725 / 2750

页数：26

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