Multivariate Operator-Self-Similar Random Fields

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.