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

Andrew Rosalsky; Lê Vǎn Thành

doi:10.3934/naco.2024010

Article Contents

2024, Volume 14, Issue 4: 724-734. Doi: 10.3934/naco.2024010

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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

Andrew Rosalsky^1, and
Lê Vǎn Thành^2, ,

1.
University of Florida, USA
2.
Vinh University, Viet Nam

^*Corresponding author: Lê Vǎn Thành
^*Corresponding author: Lê Vǎn Thành

This paper is handled by Hongwei Mei as guest editor

Received: November 2023

Revised: February 2024

Early access: March 2024

Published: December 2024

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Abstract

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.

Keywords:

Maximal inequality,
Array of Banach space valued random elements,
Martingale type p Banach space,
Mean convergence of order q,
Double sums.

Mathematics Subject Classification: Primary: 60F25; 60F99; Secondary: 60B11, 60B12.

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References

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