In this paper we construct general vector-valued infinitely-divisible independently scattered random measures with values in R m and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all integrable matrix-valued deterministic functions is characterized in terms of certain characteristics of the random measure. In addition a general construction principle is presented.

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Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields X = {X(t) : t ∈ R d } with values in 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 utilising certain homogeneous functions.

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