The Uniform Law for Sojourn Measures of Random Fields

TL;DR

This paper extends the uniform law for sojourn times from processes with cyclically exchangeable increments to more general random fields with invariant properties, broadening the applicability of these probabilistic results.

Contribution

It introduces a generalized uniform law for sojourn measures applicable to a wider class of random fields with invariance properties, expanding previous theoretical frameworks.

Findings

Extended the uniform law to random fields with invariance

Applicable to general parameter sets in random fields

Broadened understanding of sojourn time distributions

Abstract

The uniform law for sojourn times of processes with cyclically exchangeable increments is extended to the case of random fields, with general parameter sets, that possess a suitable invariance property.