Occupation measure functionals in merging phase space

This paper deals with the averaging and diffusion approximation for occupation time of general phase space semi-Markov processes under split with simple and double merging in a series scheme. These results seem to be particularly interesting since the variance coefficient is obtained in a simple for...

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2010-04, Vol.82 (2), p.149-163
Main Authors: Koroliuk, V.S., Kutoviy, O., Limnios, N.
Format: Article
Language:English
Subjects:
averaging principle
diffusion approximation
occupation measure
random evolution
semi-Markov process
singular perturbation
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Summary:This paper deals with the averaging and diffusion approximation for occupation time of general phase space semi-Markov processes under split with simple and double merging in a series scheme. These results seem to be particularly interesting since the variance coefficient is obtained in a simple form. The method of proof of weak convergence results here is based on the construction of the compensating operator of the extended Markov renewal processes and on the solution of the singular perturbation problem of this operator acting on test functions.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442500903237138