Journal of Applied Probability

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

Thomas House

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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


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