Operator-stable and operator-self-similar random fields

Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields $\mathbb{X}=\{X\left(t\right):t\in {\mathbb{R}}^d\}$ 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 utilizing certain homogeneous functions.