Lie algebra solution of population models based on time-inhomogeneous Markov chains. (English) Zbl 1319.92042

House, Thomas

J. Appl. Probab. 49, No. 2, 472-481 (2012).

Summary: 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.

MSC:

92D25	Population dynamics (general)
60J28	Applications of continuous-time Markov processes on discrete state spaces
17B80	Applications of Lie algebras and superalgebras to integrable systems

Keywords:

Lie algebra; Markov chain; time inhomogeneous; epidemic; birth-death process

Software:

Expokit

References:

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