An exponential inequality for orthomartingale differences random fields and some applications

TL;DR

This paper develops an exponential inequality for orthomartingale difference random fields and demonstrates its applications in convergence rates and invariance principles.

Contribution

It introduces a new exponential inequality specifically for orthomartingale difference random fields, advancing theoretical understanding.

Findings

Provides bounds for convergence rates in the law of large numbers

Establishes a H"olderian weak invariance principle using the inequality

Offers tools for analyzing random fields in probability theory

Abstract

In this paper, we establish an exponential inequality for random fields, which is applied in the context of convergence rates in the law of large numbers and H\"olderian weak invariance principle.