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Series in Contemporary Mathematics

Linear Stochastic Systems

A Geometric Approach to Modeling, Estimation and Identification

Authors: Lindquist, Anders, Picci, Giorgio

  • Maximizes reader insights into stochastic modeling, estimation, system identification, and time series analysis
  • Reveals the concepts of stochastic state space and state space modeling to unify the idea
  • Supports further exploration through a unified and logically consistent view of the subject
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Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-662-45750-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-662-45749-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: December 16, 2016
  • ISBN 978-3-662-52618-7
  • Free shipping for individuals worldwide
About this book

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.

Reviews

“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)


Table of contents (17 chapters)

  • Introduction

    Lindquist, Anders (et al.)

    Pages 1-23

  • Geometry of Second-Order Random Processes

    Lindquist, Anders (et al.)

    Pages 25-64

  • Spectral Representation of Stationary Processes

    Lindquist, Anders (et al.)

    Pages 65-101

  • Innovations, Wold Decomposition, and Spectral Factorization

    Lindquist, Anders (et al.)

    Pages 103-151

  • Spectral Factorization in Continuous Time

    Lindquist, Anders (et al.)

    Pages 153-174

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-662-45750-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-662-45749-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: December 16, 2016
  • ISBN 978-3-662-52618-7
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Linear Stochastic Systems
Book Subtitle
A Geometric Approach to Modeling, Estimation and Identification
Authors
Series Title
Series in Contemporary Mathematics
Series Volume
1
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-45750-4
DOI
10.1007/978-3-662-45750-4
Hardcover ISBN
978-3-662-45749-8
Softcover ISBN
978-3-662-52618-7
Series ISSN
2364-009X
Edition Number
1
Number of Pages
XV, 781
Number of Illustrations and Tables
37 b/w illustrations
Topics