# Invariance principle via orthomartingale approximation

## TL;DR

This paper establishes conditions under which stationary random fields can be approximated by orthomartingale differences, providing a key decomposition criterion and extending classical conditions to multidimensional settings.

## Contribution

It introduces a necessary and sufficient condition for the orthomartingale-coboundary decomposition and extends approximation conditions to multidimensional random fields.

## Key findings

- Established a necessary and sufficient condition for the orthomartingale-coboundary decomposition.
- Provided a sufficient condition for approximating partial sums of stationary random fields by orthomartingale differences.
- Extended classical conditions like Hannan and Maxwell-Woodroofe to multidimensional contexts.

## Abstract

We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences. This condition can be checked under multidimensional analogues of the Hannan condition and the Maxwell-Woodroofe condition.