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June 2012 Lie algebra solution of population models based on time-inhomogeneous Markov chains
Thomas House
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J. Appl. Probab. 49(2): 472-481 (June 2012). DOI: 10.1239/jap/1339878799

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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Thomas House. "Lie algebra solution of population models based on time-inhomogeneous Markov chains." J. Appl. Probab. 49 (2) 472 - 481, June 2012. https://doi.org/10.1239/jap/1339878799

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1319.92042
MathSciNet: MR2977808
Digital Object Identifier: 10.1239/jap/1339878799

Subjects:
Primary: 60J22
Secondary: 17B80 , 92D25

Keywords: birth-death process , Epidemic , Lie algebra , Markov chain , time inhomogeneous

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 2 • June 2012
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