Convergence of series of conditional expectations

被引：1
|
作者：
Peligrad, M. [1 ]
Peligrad, C. [1 ]
机构：
[1] Univ Cincinnati, Dept Math Sci, POBox 210025, Cincinnati, OH 45221 USA
来源：
STATISTICS & PROBABILITY LETTERS | 2023年 / 200卷
基金：
美国国家科学基金会;
关键词：
Almost sure convergence; Markov chains; Nonstationary sequences; Maximal inequalities; Smooth Banach spaces; BANACH-SPACES;
D O I：
10.1016/j.spl.2023.109869
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：
This paper deals with almost sure convergence for partial sums of Banach space valued random variables. The results are then applied to solve similar problems for weighted partial sums of conditional expectations. They are further used to treat partial sums of powers of a reversible Markov chain operator. The method of proof is based on martingale approximation. The conditions are expressed in terms of moments of individual summands. (c) 2023 Elsevier B.V. All rights reserved.
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