Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 411-423
doi:10.1155/S1048953398000343
On intensities of modulated Cox measures
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.
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.