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

Thomas House
Source: J. Appl. Probab. Volume 49, Number 2 (2012), 472-481.

#### 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.

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Primary Subjects: 60J22
Secondary Subjects: 17B80, 92D25
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1339878799
Digital Object Identifier: doi:10.1239/jap/1339878799
Zentralblatt MATH identifier: 06053724
Mathematical Reviews number (MathSciNet): MR2977808

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