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

[1] 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
不详
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2024, 14 (04): : 724 - 734
[2] On complete convergence in mean of normed sums of independent random elements in banach spaces
Rosalsky, A
Thanh, LV
Volodin, AI
STOCHASTIC ANALYSIS AND APPLICATIONS, 2006, 24 (01) : 23 - 35
[3] Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements
Andrew ROSALSKY
L Vn THNH
Nguyen Thi THUY
Acta Mathematica Sinica,English Series, 2024, (07) : 1727 - 1740
[4] Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements
Rosalsky, Andrew
Thanh, Le Van
Thuy, Nguyen Thi
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (07) : 1727 - 1740
[5] On almost sure and mean convergence of normed double sums of banach space valued random elements
Rosalsky, Andrew
Thanh, Le Van
STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (04) : 895 - 911
[6] Mean convergence theorems for the maximum of normed double sums of Banach space valued random elements under compact uniform integrability conditions
Rosalsky, Andrew
Thanh, Le Van
PERIODICA MATHEMATICA HUNGARICA, 2025,
[7] A WEAK LAW FOR NORMED WEIGHTED SUMS OF RANDOM ELEMENTS IN RADEMACHER TYPE-P BANACH-SPACES
ADLER, A
ROSALSKY, A
TAYLOR, RL
JOURNAL OF MULTIVARIATE ANALYSIS, 1991, 37 (02) : 259 - 268
[8] On complete convergence in mean for double sums of independent random elements in Banach spaces
Parker R.
Rosalsky A.
Lobachevskii Journal of Mathematics, 2017, 38 (1) : 177 - 191
[9] On complete convergence in mean for double sums of independent random elements in Banach spaces
L. V. Thanh
N. T. Thuy
Acta Mathematica Hungarica, 2016, 150 : 456 - 471
[10] On complete convergence in mean for double sums of independent random elements in Banach spaces
Thanh, L. V.
Thuy, N. T.
ACTA MATHEMATICA HUNGARICA, 2016, 150 (02) : 456 - 471

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