Optimization of Stochastic Systems : Topics in Discrete-Time Dynamics
There are some limit theorems and asymptotic properties of linear state space models driven by martingale differences that are presented. Because many excellent books are available on martingales and their limit theorems, derivations and proofs are mostly sketchy, and readers are referred to these sources. The results in Chapter 2 are applied in Chapters 5, 6, and 8, among other places. The notion of dynamic aggregation and its relation to cointegration and error-correction models are developed in Chapter 4. Some recursive parameter estimation schemes and their statistical properties are included in Chapters 5 and 6. Here again, books devoted entirely to these topics are available in the literature, and much had to be omitted to keep the second edition to a manageable size. In an appendix to Chapter 7, a potentially very powerful tool in proving convergence of adaptive schemes is outlined. Rational expectations models and their solution methods are developed in Chapter 8 because of their wide-spread interest to economists.
A very important class of problems in sequential decision problems revolves around questions of approximating nonlinear dynamics or more generally complex situations with a sequence of less complex ones. Chapter 9 does not begin to do justice to this class of problems but is included as being suggestive of works to be done. When I first started contemplating the revision of the first edition, I benefited from a list of excellent suggestions from Rick van der Ploeg, though I did not necessarily incorporate all of his suggestions. Conversations with Thomas Sargent and Victor Solo were useful in organizing the material into the form of the second edition. I also benefited from discussions with Hashem Pesaran and correspondences with L. Broze in finalizing Chapter 8. Some material in this book was used as lecture notes in a graduate course in the Department of Economics, University of California, Los Angeles, and the winter quarter of 1987. I thank the participants in the course for many useful comments. This major revision of the First Edition addresses optimization problems stated in stochastic difference equations, which often contain uncertain or randomly varying parameters.
It presents a set of concepts and techniques useful in analyzing or controlling stochastic dynamic processes, with possible incompletely specified characteristics. It discusses basic system properties such as: Stability and observability; Dynamic programming formulations of optimal and adaptive control problems; Parameter estimation schemes and their convergence behavior; and solution methods for rational expectations models using martingale differences.
- Hardback | 432 pages
- 152.4 x 231.1 x 25.4mm | 589.68g
- 22 Nov 1989
- Emerald Publishing Limited
- Academic Press Inc
- United Kingdom
- 2nd Revised edition
Other books in this series
02 Nov 1987
28 Apr 1989
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