Operator-stable and operator-self-similar random fields

Abstract: Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields $\mathbb{X}={X(t) : t \in \mathbb{R}^d }$ with values in $\mathbb{R}^m$ are invariant in law under operator-scaling in both the time-domain and the state-space. The construction is based on operator-stable random measures utilising certain homogeneous functions.