Martingale approximations for random fields

TL;DR

This paper establishes conditions under which random fields can be approximated by ortho-martingales in mean square, with applications to linear and nonlinear fields with independent innovations.

Contribution

It provides necessary and sufficient projective criteria for mean square martingale approximation of random fields, extending existing theory.

Findings

Derived projective criteria for approximation

Applied results to linear random fields

Extended to nonlinear random fields

Abstract

In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field with an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations.