On intensities of modulated Cox measures. (1998)

• Record Type: Journal Article
• Authors: Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 3(1998)
• Page Start: 411
• Page End: 423
• Publication Date: 1998
• Subjects: Markov modulated Poisson process -- modulated Cox measure -- Little's formula -- Campbell's formula -- potential for modulation -- semi-Markov modulated Cox process -- semiregenerative modulated Cox 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/S1048953398000343
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic process ξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure by ξ is specified for marked Cox measures. Particular cases of modulation by ξ as semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.