Multivariate Operator-Self-Similar Random Fields

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 $X=\{X(t),t\in {\mathbb{R}}^d\}$ with values in ${\mathbb{R}}^m$ are constructed by utilizing homogeneous functions and stochastic integral representations.