Multivariate operator-self-similar random fields

Multivariate random fields whose distributions are invariant under operator-scalings in both the time domain and the 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 ∈ R d } with values in R m are constructed by utilizing homogeneous functions and stochastic integral representations.