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# Linear Stochastic Systems

### by Peter E. Caines

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2018 / xviii + 874 pages / Softcover / ISBN 978-1-611974-70-6 / List Price $89.00 / SIAM Member Price$62.30 / Order Code CL77

Keywords: stochastic systems, linear systems, control theory, filtering and state estimation, system identification, adaptive control, optimal control

Contents
Preface to the Classics Edition;
Preface;
Chapter 0: Introduction;
Chapter 1: Stochastic Processes;
Chapter 2: Linear Stochastic Systems;
Chapter 3: Estimation Theory;
Chapter 4: Stochastic Realization Theory;
Chapter 5: System Identification: Foundations and Basic Concepts;
Chapter 6: Least Squares Parameter Estimation;
Chapter 7: Maximum Likelihood Estimation of Gaussian ARMAX and State-Space Systems;
Chapter 8: Minimum Prediction Error Identification Methods;
Chapter 9: Nonstationary System Identification;
Chapter 10: Feedback, Causality, and Closed Loop System Identification;
Appendices;
Appendix 1: Probability Theory;
Appendix 2: System Theory;
Appendix 3: Harmonic and Related Analysis;
References;
Index.

Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships.

The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including

• the fundamentals of stochastic processes and the construction of stochastic systems;
• an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and
• a presentation of stochastic adaptive control theory.

Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.

Audience
This book is written for graduate students, teachers, and research workers in the areas of systems and control theory and its application, probability and statistics, time-series analysis, econometrics, and related areas.