| Article ID: | iaor19992107 |
| Country: | United States |
| Volume: | 11 |
| Issue: | 3 |
| Start Page Number: | 411 |
| End Page Number: | 423 |
| Publication Date: | Jul 1998 |
| Journal: | Journal of Applied Mathematics and Stochastic Analysis |
| Authors: | Dshalalow Jewgeni H. |
| Keywords: | probability |
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.