Choquet random sup-measures with aggregations

TL;DR

This paper introduces a variation of Choquet random sup-measures that serve as scaling limits for aggregated models, highlighting their unique distributional properties and including stable-regenerative cases.

Contribution

The paper presents a new class of Choquet random sup-measures arising from aggregation, expanding the understanding of their distributional behavior and connections to stable-regenerative models.

Findings

Introduced a new variation of Choquet random sup-measures.

Demonstrated these measures as scaling limits of empirical models.

Showed their finite-dimensional distributions differ from classical extreme-value distributions.

Abstract

A variation of Choquet random sup-measures is introduced. These random sup-measures are shown to arise as the scaling limits of empirical random sup-measures of a general aggregated model. Because of the aggregations, the finite-dimensional distributions of introduced random sup-measures do not necessarily have classical extreme-value distributions. Examples include the recently introduced stable-regenerative random sup-measures as a special case.