On modulated random measures. (1991) - Dshalalow, Jewgeni H.
Abstract : In this paper the author introduces the notion of a modulated marked random measure, Z ξ, 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 = lim t → ∞ 1 t E [ Z ξ ( [ 0, t ] ) ] are evaluated in terms of parameters of ξ . Examples and applications to inventories, queueing processes and economics are discussed.