Markov Chain Process (Theory and Cases)

Matrix Models

Author(s): Carlos Polanco *

Pp: 8-21 (14)

DOI: 10.2174/9789815080476123010007

* (Excluding Mailing and Handling)

Abstract

This chapter describes and provides an example of the matrix models: Lefkovitch model, Leslie model, Malthus model, and stability matrix models. From these the Discrete- and Continuous-Time Markov Chain Process is introduced. These matrix models are presented as they were historically occurring, and it is highlighted how the matrix structure offers a simple algebraic solution to problems involving multiple variables, where the elements of those matrices are conditional probabilities when going from a state A (row i) to a state B (column j). Once these matrix models have been defined and exemplified, it is shown that the eigenvalues and eigenvectors of the conditional probability matrix determine the long-term stability matrix of the Markov Chain Process.


Keywords: Continuous-Time Markov Chain Process, Discrete-Time Markov Chain Process, Eigenvalues, Eigenvectors, Lefkovitch Model, Leslie Model, Malthus Model, Stability Matrix Models.

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