Maximal inequalities and convergence results on multidimensionally indexed demimartingales

TL;DR

This paper extends maximal inequalities and convergence results to multidimensionally indexed demimartingales, filling a gap in the literature for multiindexed random variables.

Contribution

It introduces new maximal inequalities and asymptotic results for multidimensionally indexed demimartingales, a less-studied class of random variables.

Findings

Established maximal probability inequalities for multidimensional demimartingales.

Derived moment inequalities and convergence results for these processes.

Extended classical inequalities to a multiindexed setting.

Abstract

We obtain some maximal probability and moment inequalities for multidimensionally indexed demimartingales. Although the class of single-indexed demimartingales has been studied extensively, no significant amount of work has been done for the corresponding multiindexed class of random variables. This work aims to fill in this gap in the literature by extending well-known inequalities and asymptotic results to this more general class of random variables.