Multivariate stochastic integrals with respect to independently scattered random measures on δ-rings

Abstract

In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in ${\mathbb{R}}^m$ 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.