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

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE Finance and Stochastics Pub Date : 2022-11-17 DOI:10.1080/17442508.2022.2147006

Zong-feng Qi, Jinyu Zhou, Jigao Yan

引用次数: 1

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.

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鞅差分序列随机加权和最大值的完全矩收敛性

在适当的充分条件下，研究了鞅差分序列随机加权和的极大值完全矩收敛性和随机索引和的完全矩收敛性。得到了MDS的Marcinkiewicz-Zygmund型强大数定律(MZSLLN)。此外，从某种意义上揭示了权重、权重函数和边界函数之间的关系。本文的结果推广了一些独立和相关随机变量的相应结果。作为应用，建立了非参数回归模型中估计量的强相合性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.

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