Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 411-423

On intensities of modulated Cox measures

Jewgeni H. Dshalalow

Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 1 April 1997; Revised 1 March 1998

Copyright © 1998 Jewgeni H. Dshalalow. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.