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Journal of Applied Mathematics and Stochastic Analysis
Volume 4, Issue 4, Pages 305-312
http://dx.doi.org/10.1155/S1048953391000230

On modulated random measures

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

Received 1 March 1991; Revised 1 August 1991

Copyright © 1991 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.

Abstract

In this paper the author introduces the notion of a modulated marked random measure, Zξ, on the class of locally compact and σ-compact spaces with countable bases. As special cases, are marked processes modulated by ξ are considered where ξ is a semi-Markov or semi-regenerative process. For either case, the intensities k=limt1tE[Zξ([0,t])] are evaluated in terms of parameters of ξ. Examples and applications to inventories, queueing processes and economics are discussed.