Reduction principle for functionals of vector random fields

TL;DR

This paper establishes a reduction principle for functionals of vector long-range dependent random fields with diverse component behaviors, supported by theoretical proofs, simulations, and an application to Minkowski functionals.

Contribution

It introduces a novel reduction principle applicable to vector random fields with varying long-range dependence, expanding the understanding of their functional behaviors.

Findings

Theoretical proof of the reduction principle for vector fields.

Simulation results confirm the theoretical predictions.

Application to Minkowski functionals demonstrates practical relevance.

Abstract

We prove a version of the reduction principle for functionals of vector long-range dependent random fields. The components of the fields may have different long-range dependent behaviours. The results are illustrated by an application to the first Minkowski functional of the Fisher-Snedecor random fields. Simulation studies confirm the obtained theoretical results and suggest some new problems.