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A bivariate counting process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Ray Watson  and
Paul Yip
Ray Watson*
Affiliation:
University of Melbourne
Paul Yip*
Affiliation:
University of Hong Kong
*
∗ Postal address: Department of Statistics, University of Melbourne, Parkville, VIC 3052, Australia.
∗∗ Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

We consider a bivariate Markov counting process with transition probabilities having a particular structure, which includes a number of useful population processes. Using a suitable random time-scale transformation, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using martingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.

Keywords

POPULATION PROCESSRANDOM TIME-SCALE TRANSFORMATIONMARTINGALEINFERENCE

MSC classification

Primary: 60J99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 353 - 364
Copyright
Copyright © Applied Probability Trust 1993 

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References

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