On modulated random measures (Q1180691)

Summary: The author introduces the notion of a modulated marked random measure, \(Z^ \xi\), on the class of locally compact and \(\sigma\)-compact spaces with countable bases. As special cases, marked processes modulated by \(\xi\) are considered where \(\xi\) is a semi-Markov or semi-regenerative process. For either case, the intensities \(\kappa=\lim_{t\to\infty}{1\over t}E[Z^ \xi([0,t])]\) are evaluated in terms of parameters of \(\xi\). Examples and applications to inventories, queueing processes and economics are discussed.