## Journal of Applied Probability

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

### Approximations: replacing random variables with their means

#### 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