Multivariate Operator-Self-Similar Random Fields

TL;DR

This paper investigates multivariate operator-self-similar random fields, characterizing their scaling operators and constructing two classes of stable fields using homogeneous functions and stochastic integrals.

Contribution

It introduces a comprehensive characterization of operator-self-similar random fields and constructs new classes of stable fields with operator-scaling properties.

Findings

Characterization of scaling operators for operator-self-similar fields

Construction of two classes of stable operator-self-similar fields

Use of homogeneous functions and stochastic integrals in constructions

Abstract

Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields $X=\{X(t), t \in \R^d\}$ with values in $\R^m$ are constructed by utilizing homogeneous functions and stochastic integral representations.