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Linear Stochastic Systems

A Geometric Approach to Modeling, Estimation and Identification

  • Anders Lindquist
  • Giorgio Picci

Part of the Series in Contemporary Mathematics book series (SCMA, volume 1)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Anders Lindquist, Giorgio Picci
    Pages 1-23
  3. Anders Lindquist, Giorgio Picci
    Pages 25-64
  4. Anders Lindquist, Giorgio Picci
    Pages 65-101
  5. Anders Lindquist, Giorgio Picci
    Pages 103-151
  6. Anders Lindquist, Giorgio Picci
    Pages 153-174
  7. Anders Lindquist, Giorgio Picci
    Pages 175-213
  8. Anders Lindquist, Giorgio Picci
    Pages 215-250
  9. Anders Lindquist, Giorgio Picci
    Pages 251-311
  10. Anders Lindquist, Giorgio Picci
    Pages 313-353
  11. Anders Lindquist, Giorgio Picci
    Pages 355-412
  12. Anders Lindquist, Giorgio Picci
    Pages 413-462
  13. Anders Lindquist, Giorgio Picci
    Pages 463-506
  14. Anders Lindquist, Giorgio Picci
    Pages 507-542
  15. Anders Lindquist, Giorgio Picci
    Pages 543-590
  16. Anders Lindquist, Giorgio Picci
    Pages 591-636
  17. Anders Lindquist, Giorgio Picci
    Pages 637-673
  18. Anders Lindquist, Giorgio Picci
    Pages 675-724
  19. Back Matter
    Pages 725-781

About this book

Introduction

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 notion of 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.

Keywords

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

Authors and affiliations

  • Anders Lindquist
    • 1
  • Giorgio Picci
    • 2
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of Information EngineeringUniversity of PadovaPadovaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-45750-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-45749-8
  • Online ISBN 978-3-662-45750-4
  • Series Print ISSN 2364-009X
  • Series Online ISSN 2364-0103
  • Buy this book on publisher's site
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