Multivariate tempered stable random fields

TL;DR

This paper constructs multivariate tempered stable random measures and characterizes their integrable function spaces, introducing operator-fractional tempered stable random fields with specific representations.

Contribution

It introduces multivariate tempered stable random measures and characterizes their integrable functions, along with new operator-fractional tempered stable random fields with explicit representations.

Findings

Characterization of integrable functions via quasi-norms

Construction of operator-fractional tempered stable random fields

Representation of these fields through moving-average and harmonizable forms

Abstract

Multivariate tempered stable random measures (ISRMs) are constructed and their corresponding space of integrable functions is characterized in terms of a quasi-norm utilizing the so-called Rosinski measure of a tempered stable law. In the special case of exponential tempered ISRMs operator-fractional tempered stable random fields are presented by a moving-average and a harmonizable representation, respectively.