## Journal of Applied Probability

- J. Appl. Probab.
- Volume 49, Number 2 (2012), 472-481.

### Lie algebra solution of population models based on time-inhomogeneous Markov chains

#### Abstract

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical, and social applications. In this paper we present the Lie algebraic method, and apply it to three biologically well-motivated examples. The result of this is a solution form that is often highly computationally advantageous.

#### Article information

**Source**

J. Appl. Probab., Volume 49, Number 2 (2012), 472-481.

**Dates**

First available in Project Euclid: 16 June 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1339878799

**Digital Object Identifier**

doi:10.1239/jap/1339878799

**Mathematical Reviews number (MathSciNet)**

MR2977808

**Zentralblatt MATH identifier**

1319.92042

**Subjects**

Primary: 60J22: Computational methods in Markov chains [See also 65C40]

Secondary: 17B80: Applications to integrable systems 92D25: Population dynamics (general)

**Keywords**

Lie algebra Markov chain time inhomogeneous epidemic birth-death process

#### Citation

House, Thomas. Lie algebra solution of population models based on time-inhomogeneous Markov chains. J. Appl. Probab. 49 (2012), no. 2, 472--481. doi:10.1239/jap/1339878799. https://projecteuclid.org/euclid.jap/1339878799