Strong laws of large numbers for WAPND Banach-valued random elements

Abstract

In this article, we first prove Borel–Cantelli lemma and some strong laws of large numbers for APND random variables. Then, we introduce a new class of dependent random elements, called briefly WAPND, taking values in a separable Banach space. For this new class, we extend some strong laws of large numbers.

Keywords:

• Borel–Cantelli lemma
• separable Banach space
• random element
• asymptotically
• pairwise negatively dependent
• weakly asymptotically pairwise negatively dependent

AMS SUBJECT CLASSIFICATION:

• 60F15
• 60B11

Acknowledgment

The authors thank the reviewer(s) for the careful reading of the manuscript and several useful comments.