On modulated random measures

Abstract

In this paper the author introduces the notion of a modulated marked random measure, Zξ, on the class of locally compact and σ-compact spaces with countable bases. As special cases, are marked processes modulated by ξ are considered where ξ is a semi-Markov or semi-regenerative process. For either case, the intensities k=limt→∞1tE[Zξ([0,t])] are evaluated in terms of parameters of ξ. Examples and applications to inventories, queueing processes and economics are discussed.