Linear Stochastic Systems

1. Front Matter

   Pages i-xv

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2. Introduction

   • Anders Lindquist, Giorgio Picci

   Pages 1-23

3. Geometry of Second-Order Random Processes

   • Anders Lindquist, Giorgio Picci

   Pages 25-64

4. Spectral Representation of Stationary Processes

   • Anders Lindquist, Giorgio Picci

   Pages 65-101

5. Innovations, Wold Decomposition, and Spectral Factorization

   • Anders Lindquist, Giorgio Picci

   Pages 103-151

6. Spectral Factorization in Continuous Time

   • Anders Lindquist, Giorgio Picci

   Pages 153-174

7. Linear Finite-Dimensional Stochastic Systems

   • Anders Lindquist, Giorgio Picci

   Pages 175-213

8. The Geometry of Splitting Subspaces

   • Anders Lindquist, Giorgio Picci

   Pages 215-250

9. Markovian Representations

   • Anders Lindquist, Giorgio Picci

   Pages 251-311

10. Proper Markovian Representations in Hardy Space

    • Anders Lindquist, Giorgio Picci

    Pages 313-353

11. Stochastic Realization Theory in Continuous Time

    • Anders Lindquist, Giorgio Picci

    Pages 355-412

12. Stochastic Balancing and Model Reduction

    • Anders Lindquist, Giorgio Picci

    Pages 413-462

13. Finite-Interval and Partial Stochastic Realization Theory

    • Anders Lindquist, Giorgio Picci

    Pages 463-506

14. Subspace Identification of Time Series

    • Anders Lindquist, Giorgio Picci

    Pages 507-542

15. Zero Dynamics and the Geometry of the Riccati Inequality

    • Anders Lindquist, Giorgio Picci

    Pages 543-590

16. Smoothing and Interpolation

    • Anders Lindquist, Giorgio Picci

    Pages 591-636

17. Acausal Linear Stochastic Models and Spectral Factorization

    • Anders Lindquist, Giorgio Picci

    Pages 637-673

18. Stochastic Systems with Inputs

    • Anders Lindquist, Giorgio Picci

    Pages 675-724

19. Back Matter

    Pages 725-781

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This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notionof the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.

• Markovian Representations
• Splitting Subspaces
• Stochastic Systems
• Wold Decomposition
• modeling of stationary random signals
• second order stationary processes

“The purpose of this book is to present the mathematical background necessary for understanding the linear state-space modeling of second-order random processes and its applications to estimation and identification theory. … this monograph is an excellent reference for researchers interested in geometric theory of stochastic realization and its applications.” (Viorica M. Ungureanu, Mathematical Reviews, January, 2016)

• Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

  Anders Lindquist

• Department of Information Engineering, University of Padova, Padova, Italy

  Giorgio Picci

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