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∈Rd}X={X(t),t∈Rd} with values in RmRm are constructed by utilizing homogeneous functions and stochastic integral representations.