Scaling transition for nonlinear random fields with long-range dependence

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 Puplinskaitė and Surgailis (2016), Puplinskaitė and Surgailis (2015).

References in corpus (4)

• Central limit theorems for sequences of multiple stochastic integrals
• Central limit theorems for long range dependent spatial linear processes
• Sample autocovariances of long-memory time series
• Anisotropic scaling of random grain model with application to network traffic

Cited by in corpus (8)

• Some remarks on scaling transition in limit theorems for random fields
• Operator-scaling Gaussian random fields via aggregation
• Limit theorems for $p$-domain functionals of stationary Gaussian fields
• Gaussian self-similar random fields with distinct stationary properties of their rectangular increments
• Scaling transition and edge effects for negatively dependent linear random fields on ${\mathbb{Z}}^2$
• Scaling limits of linear random fields on ${\mathbb{Z}}^2$ with general dependence axis
• Local scaling limits of Lévy driven fractional random fields
• Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence