Sojourn measures of Student and Fisher-Snedecor random fields

TL;DR

This paper establishes limit theorems for the volumes of excursion sets of Student and Fisher-Snedecor random fields, including generalizations to moving levels and cross-correlated cases, supported by simulations.

Contribution

It introduces new limit theorems for sojourn measures of Student and Fisher-Snedecor fields, extending previous results to dependent, heavy-tailed, and cross-correlated scenarios.

Findings

Proved limit theorems for excursion set volumes

Extended results to moving levels and cross-correlated fields

Provided simulation validation

Abstract

Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special attention is paid to Student and Fisher-Snedecor random fields. Some simulation results are also presented.