Integrability conditions for Compound Random Measures
Alan Riva Palacio, Fabrizio Leisen
TL;DR
This paper establishes conditions for the existence of Compound Random Measures (CoRM's) and explores their properties under specific mathematical settings, enhancing understanding of their theoretical foundations.
Contribution
It provides new existence conditions and analyzes properties of CoRM's with exponential scores and regularly varying Lévy intensities.
Findings
Conditions for CoRM existence established
Properties of CoRM with exponential scores analyzed
Behavior under regularly varying Lévy intensities characterized
Abstract
Compound random measures (CoRM's) are a flexible and tractable framework for vectors of completely random measure. In this paper, we provide conditions to guarantee the existence of a CoRM. Furthermore, we prove some interesting properties of CoRM's when exponential scores and regularly varying L\'evy intensities are considered.
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