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On reinforcement-depletion compartmental urn models

Published online by Cambridge University Press:  14 July 2016

Peter Donnelly  and
Ward Whitt
Peter Donnelly*
Affiliation:
Queen Mary College, University of London
Ward Whitt*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, London El 4NS, UK.
∗∗Postal address: AT&T Bell Laboratories, Room 2C-178, Murray Hill, NJ 07974, USA.
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Abstract

We verify and extend a conjecture of Purdue (1981) concerning the stochastic monotonicity of absorption times in a class of compartmental urn models. We also describe the effect of increased variability in the reinforcement sizes. Finally, we investigate variability in the content process for large populations. In many applications, compartmental models substantially under-represent the variability observed in the data, so that there has been considerable interest in modifying the model to increase the variability. We show that the squared coefficient of variation of the content is not asymptotically negligible when both the size and the variability of the reinforcements are of the same order as the initial population.

Keywords

COMPARTMENTAL MODELSFIRST-PASSAGE TIMESSTOCHASTIC ORDERCOUPLINGMAJORIZATIONLIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 477 - 489
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Partially supported by the U.S. National Science Foundation under Grant No. DMS-86–08857.

References

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