MAXIMAL INEQUALITIES FOR NORMED DOUBLE SUMS OF RANDOM ELEMENTS IN MARTINGALE TYPE p BANACH SPACES WITH APPLICATIONS TO DEGENERATE MEAN CONVERGENCE OF THE MAXIMUM OF NORMED SUMS

被引：1

作者：

Rosalsky, Andrew ^{[1
]}

Thanh, Le Van ^{[2
]}

机构：

[1] Univ Florida, Immokalee, FL USA

[2] Vinh Univ, Vinh, Vietnam

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2024年

关键词：

Maximal inequality; Array of Banach space valued random elements; Martingale type p Banach space; Mean convergence of order q; Double sums; LARGE NUMBERS; WEIGHTED SUMS; DOUBLE ARRAYS; LAW; THEOREM; VALUES; SURE;

D O I：

10.3934/naco.2024010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this correspondence, we prove new maximal inequalities for normed double sums of random elements taking values in a real separable martingale type p Banach space. The result is then applied to establish mean convergence theorems for the maximum of normed and suitably centered double sums of Banach space-valued random elements.

引用

页数：11

共 45 条

[11] Almost sure summability of the maximal normed partial sums of m-dependent random elements in Banach spaces
Lê Vǎn Thành
Archiv der Mathematik, 2024, 122 : 203 - 212
[12] Almost sure summability of the maximal normed partial sums of m-dependent random elements in Banach spaces
Thanh, Le Van
ARCHIV DER MATHEMATIK, 2024, 122 (02) : 203 - 212
[13] Optimal moment conditions for complete convergence for maximal normed weighted sums from arrays of rowwise independent random elements in Banach spaces
Rosalsky, Andrew
Thanh Le Van
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (03)
[14] Optimal moment conditions for complete convergence for maximal normed weighted sums from arrays of rowwise independent random elements in Banach spaces
Andrew Rosalsky
Lê Vǎn Thành
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117
[15] A weak law with random indices for randomly weighted sums of random elements in martingale type p banach spaces
Rosalsky, A
Sreehari, M
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (02) : 1257 - 1270
[16] Complete convergence theorems for weighted row sums from arrays of random elements in Rademacher type p and martingale type p Banach spaces
Hu, Tien-Chung
Rosalsky, Andrew
Volodin, Andrei
STOCHASTIC ANALYSIS AND APPLICATIONS, 2019, 37 (06) : 1092 - 1106
[17] Mean Convergence Theorems for the Maximum Normed Partial Sums of Random Vectors in Hilbert Spaces under a General Condition of Weighted Integrability
Anh, Vo Thi Van
Tu, Nguyen Ngoc
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2024, 45 (09) : 4018 - 4025
[18] Mean convergence theorems with or without random indices for randomly weighted sums of random elements in rademacher type p banach spaces
Rosalsky, A
Sreehari, M
Volodin, AI
STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (05) : 1169 - 1187
[19] On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces
Hong, DH
Cabrera, MO
Sung, SH
Volodin, AI
STATISTICS & PROBABILITY LETTERS, 2000, 46 (02) : 177 - 185
[20] CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENTS IN P-TYPE SPACES
VOLODIN, AI
IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1990, (10): : 65 - 67

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