Infinite divisibility of random fields admitting an integral representation with an infinitely divisible integrator

TL;DR

This paper proves that random fields represented as integrals with respect to infinitely divisible measures are themselves infinitely divisible, expanding understanding of their probabilistic structure.

Contribution

It establishes the infinite divisibility of a broad class of random fields constructed via integral representations with infinitely divisible integrators.

Findings

Random fields with integral representations are infinitely divisible.

The result applies to a wide class of stochastic processes.

Provides theoretical foundation for modeling with infinitely divisible fields.

Abstract

We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.