International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1998 / Article

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Volume 11 |Article ID 380527 | 13 pages | https://doi.org/10.1155/S1048953398000343

On intensities of modulated Cox measures

Jewgeni H. Dshalalow1

1Department of Applied Mathematics, Florida Institute of Technology, USA

Received01 Apr 1997
Revised01 Mar 1998

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.

Copyright © 1998 Hindawi Publishing Corporation. 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.

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