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Lie Algebra Solution of Population Models Based on Time-Inhomogeneous Markov Chains

Part of: Lie algebras and Lie superalgebras Markov processes

Published online by Cambridge University Press:  04 February 2016

Thomas House
Thomas House*
Affiliation:
University of Warwick
*
∗ Postal address: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. Email address: t.a.house@warwick.ac.uk
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Abstract

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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.

Keywords

Lie algebraMarkov chaintime inhomogeneousepidemicbirth-death process

MSC classification

Primary: 60J22: Computational methods in Markov chains
Secondary: 17B80: Applications to integrable systems 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 472 - 481
Copyright
© Applied Probability Trust 

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