Journal of Applied Probability

Approximations: replacing random variables with their means

Joe Gani


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

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

First available in Project Euclid: 2 December 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Markov chain random variable mean approximation


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

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