A maximal inequality for dependent random variables

TL;DR

This paper establishes a maximal inequality for dependent random variables with finite expectation, which is then used to prove a strong law of large numbers for such dependent sequences.

Contribution

It introduces a new maximal inequality applicable to dependent variables and leverages it to derive a strong law of large numbers, extending classical results.

Findings

Maximal inequality for dependent variables proved

Strong law of large numbers established for dependent sequences

Applicable to sequences with finite expected values

Abstract

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of random variables satisfying $\mathbb{E} \lvert X_{n} \rvert < \infty$ for all $n \geqslant 1$, a maximal inequality is established, and used to obtain strong law of large numbers for dependent random variables.