Journal of Applied Probability

Approximations: replacing random variables with their means

Joe Gani

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 57-62.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528466

Digital Object Identifier
doi:10.1239/jap/1417528466

Mathematical Reviews number (MathSciNet)
MR3317349

Zentralblatt MATH identifier
1318.60077

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G07: General theory of processes

Keywords
Markov chain random variable mean approximation

Citation

Gani, Joe. Approximations: replacing random variables with their means. J. Appl. Probab. 51A (2014), 57--62. doi:10.1239/jap/1417528466. https://projecteuclid.org/euclid.jap/1417528466


Export citation

References

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