On modulated random measures. (1991)

• Record Type: Journal Article
• Authors: Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 4:Number 4(1991)
• Page Start: 305
• Page End: 312
• Publication Date: 1991
• Subjects: random measure -- modulated marked random measure -- marked process -- semi-Markov process -- semi-regenerative process; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953391000230
• Languages: English
• ISSNs: 1048-9533

Abstract

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.