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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 95, 2023 - Issue 5
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Research Article

Complete moment convergence for maximum of randomly weighted sums of martingale difference sequences

Zongfeng Qia Stat Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System(CEMEE), Luoyang, People's Republic of ChinaView further author information
,
Jinyu Zhoub School of Mathematical Sciences, Soochow University, Suzhou, People's Republic of ChinaView further author information
&
Jigao Yanb School of Mathematical Sciences, Soochow University, Suzhou, People's Republic of ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9800-0230View further author information
ORCID Icon
Pages 941-961 | Received 08 Apr 2022, Accepted 31 Oct 2022, Published online: 17 Nov 2022
 
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Abstract

In this paper, complete moment convergence for maximum of randomly weighted sums and complete convergence for randomly indexed sums of martingale difference sequences (MDS) are investigated under some proper and sufficient conditions. A Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for MDS is obtained. In addition, relationships among weights, weight functions and boundary functions are revealed in a sense. The results obtained in the paper generalize some corresponding ones for independent and some dependent random variables. As an application, strong consistency for estimators in a nonparametric regression model is established.

MSC 2010:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was Supported by the National Natural Science Foundation of China [grant number 11701403].

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