Scaling transition for nonlinear random fields with long-range dependence

TL;DR

This paper characterizes the anisotropic scaling limits and transition phenomena for nonlinear functions of stationary linear random fields on b2, extending previous linear case results to nonlinear settings with different decay rates.

Contribution

It provides a complete description of scaling limits and transition phenomena for nonlinear random fields with anisotropic decay, extending prior linear field results.

Findings

Complete description of anisotropic scaling limits

Existence of scaling transition in nonlinear fields

Extension of linear results to nonlinear cases

Abstract

We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for nonlinear functions (Appell polynomials) of stationary linear random fields on $\mathbb{Z}^2$ with moving average coefficients decaying at possibly different rate in the horizontal and vertical direction. The paper extends recent results on scaling transition for linear random fields in Puplinskait\.e and Surgailis (2016), Puplinskait\.e and Surgailis (2015).