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Approximations: replacing random variables with their means

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Joe Gani
Joe Gani*
Affiliation:
Mathematical Sciences Institute, The Australian National University, Bldg 26B, Canberra ACT 0200, Australia
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Abstract

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One of the standard methods for approximating a bivariate continuous-time Markov chain {X(t), Y(t): t ≥ 0}, which proves too difficult to solve in its original form, is to replace one of its variables by its mean, This leads to a simplified stochastic process for the remaining variable which can usually be solved, although the technique is not always optimal. In this note we consider two cases where the method is successful for carrier infections and mutating bacteria, and one case where it is somewhat less so for the SIS epidemics.

Keywords

Markov chainrandom variablemeanapproximation

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G07: General theory of processes
Type
Part 3. Biological applications
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 57 - 62
Copyright
Copyright © Applied Probability Trust 2014 

References

Bailey, N. T. J. (1975). The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Hafner Press, New York.Google Scholar
Daley, D. J., and Gani, J. (1999). Epidemic Modelling: an Introduction. Cambridge University Press.Google Scholar