LEADER 04872nam 22006735 450 001 9910299783703321 005 20220818050437.0 010 $a3-662-45750-4 024 7 $a10.1007/978-3-662-45750-4 035 $a(CKB)3710000000402881 035 $a(EBL)2096165 035 $a(SSID)ssj0001501576 035 $a(PQKBManifestationID)11968031 035 $a(PQKBTitleCode)TC0001501576 035 $a(PQKBWorkID)11446469 035 $a(PQKB)11267930 035 $a(DE-He213)978-3-662-45750-4 035 $a(MiAaPQ)EBC2096165 035 $a(PPN)185488749 035 $a(EXLCZ)993710000000402881 100 $a20150424d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Stochastic Systems $eA Geometric Approach to Modeling, Estimation and Identification /$fby Anders Lindquist, Giorgio Picci 205 $a1st ed. 2015. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015. 215 $a1 online resource (788 p.) 225 1 $aContemporary mathematics,$x2364-009X ;$x0271-4132$v1 300 $aDescription based upon print version of record. 311 $a3-662-45749-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. 330 $aThis book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory. 410 0$aContemporary mathematics,$x2364-009X$x0271-4132$v1 606 $aSystem theory 606 $aProbabilities 606 $aControl engineering 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 615 0$aSystem theory. 615 0$aProbabilities. 615 0$aControl engineering. 615 14$aSystems Theory, Control. 615 24$aProbability Theory and Stochastic Processes. 615 24$aControl and Systems Theory. 676 $a510 676 $a515.724 676 $a519 676 $a519.2 700 $aLindquist$b Anders$4aut$4http://id.loc.gov/vocabulary/relators/aut$0447862 702 $aPicci$b Giorgio$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299783703321 996 $aLinear Stochastic Systems$92521522 997 $aUNINA