Multi operator-stable random measures and fields

TL;DR

This paper introduces vector-valued multi operator-stable random measures and fields, providing their construction, properties, and a moving-average representation that generalizes operator-stability and self-similarity in stochastic processes.

Contribution

It develops the theory of multi operator-stable measures and fields, including their construction, function space characterization, and a novel moving-average representation.

Findings

Constructed vector-valued multi operator-stable random measures.

Characterized the space of integrable functions via a quasi-norm.

Presented a multi operator-stable moving-average representation of a random field.

Abstract

In this paper we construct vector-valued multi operator-stable random measures that behave locally like operator-stable random measures. The space of integrable functions is characterized in terms of a certain quasi-norm. Moreover, a multi operator- stable moving-average representation of a random field is presented which behaves locally like an operator-stable random field which is also operator-self-similar.