Random Dynamical Systems – Theory and Applications

Citation

Hutton, D.M. (2011), "Random Dynamical Systems – Theory and Applications", Kybernetes, Vol. 40 No. 1/2, pp. 338-339. https://doi.org/10.1108/03684921111118086

Cyberneticians and systemists have a particular interest in random dynamical systems and any book that attempts to clarify random processes in a truly theoretical and rigorous way is worth considering, and at this price a good candidate for one's own bookshelf.

Apart from its theoretical approach, it also includes a good introduction to deterministic dynamical systems as well as a discussion on deterministic dynamical systems.

Much of the text will also be of value to economists who look to apply some of the results presented to research and development of economic models.

The book is well structured and its chapters provide continuity of interest. For example:

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  Chapter 1 provides results about the theory of determined dynamical systems/with economics applications.

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  Chapter 2 considers irreducible Markov processes.

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  In Chapters 3‐5, equilibrium and long‐run stability of a dynamical system (where the law of motion is subject to random perturbations) are featured.

All the chapters provide sample problems and are clearly presented to the reader who also has the benefit of the appendix if in doubt about any of the underlying mathematics.

As expected in this field, it is essential to provide an extensive bibliography and the authors have obviously spent much time in preparing one for this book.

The last part of the book is devoted to showing how a class of dynamic programming problems could produce dynamical systems. For many readers, the applications presented justify the introduction of the theoretical content of the earlier chapters.

The authors have provided a useful mix of theory and application which will encourage many researchers in a number of fields, particularly in mathematics and economics, as well as in cybernetics and systems, to study their offering. Although the book was compiled four years ago, it is still relevant but, of course the bibliography and some of the text might be revised for any future editions.