On Lamperti transformation and characterisations of discrete random fields

TL;DR

This paper explores the relationships between stationary discrete fields, increment fields, and self-similar fields using difference equations and Lamperti transformation, extending previous results from stationary processes.

Contribution

It generalizes recent findings by characterizing discrete stationary fields through difference equations involving self-similar and stationary increment fields.

Findings

Established connections between stationary and self-similar fields.

Extended Lamperti transformation to discrete random fields.

Provided a unified framework for different classes of discrete fields.

Abstract

In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and, through Lamperti transformation, self-similar fields. Our contribution is a natural generalisation of recently proved results covering the case of stationary processes.