Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 4, Pages 305-312
doi: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 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 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=limt→∞1tE[Zξ([0,t])] are evaluated in terms of
parameters of ξ. Examples and applications to inventories, queueing processes
and economics are discussed.