Linear stochastic systems [electronic resource] : a geometric approach to modeling, estimation and identification / Anders Lindquist, Giorgio Picci.
Lindquist, Anders, author.; Picci, Giorgio, 1942- author.
2015
QA402
Available Online

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Title Linear stochastic systems [electronic resource] : a geometric approach to modeling, estimation and identification / Anders Lindquist, Giorgio Picci.
Author Lindquist, Anders, author.
ISBN 9783662457504 electronic book
3662457504 electronic book
9783662457498
DOI https://doi.org/10.1007/978-3-662-45750-4
Published Heidelberg : Springer, 2015.
Language English
Description 1 online resource : illustrations.
Item Number 10.1007/978-3-662-45750-4 doi
Call Number QA402
Dewey Decimal Classification 519.2
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (viewed April 30, 2015).
Added Author Picci, Giorgio, 1942- author.
Series Series in contemporary mathematics (Springer (Firm)) ; v. 1.
Available in Other Form Print version: 9783662457498
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Introduction
Geometry of Second-Order Random Processes
Spectral Representation of Stationary Processes
Innovations, Wold Decomposition, and Spectral Factorization
Wold Decomposition and Spectral Factorization in Continuous Time
Linear Finite-Dimensional Stochastic Systems
The Geometry of Splitting Subspaces
Markovian Representations
Proper Markovian Representations in Hardy Space
Stochastic Realization Theory in Continuous Time
Stochastic Balancing and Model Reduction
Finite-Interval Stochastic Realization and Partial Realization Theory
Subspace Identification for Time Series
Zero Dynamics and the Geometry of the Riccati Inequality
Smoothing and Interpolation
Acausal Linear Stochastic Models and Spectral Factorization
Stochastic Systems with Inputs
Appendix A. Basic Principles of Deterministic Realization Theory
Appendix B. Some Topics in Linear Algebra and Hilbert Space Theory.

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