Stochastic Systems: The Mathematics of Filtering and Identification and Applications

1. Front Matter

   Pages i-xii

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2. The Main Themes of the ASI “Stochastic System: The Mathematics of Filtering and Identification and Applications”

   1. Front Matter

      Pages 1-1

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   2. Introduction: An Annotated Navigation Chart and Sketch of the Main Themes in this Volume and their Interrelations

      • Michiel Hazewinkel, Jan C. Willems

      Pages 3-26

3. Introductory Tutorial Material for Identification and Filtering Problems

   1. Front Matter

      Pages 27-27

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   2. The LQG-Problem: A Brief Tutorial Exposition

      • Jan C. Willems

      Pages 29-44

   3. A Tutorial Article on the Itô Integral and the Stochastic Calculus

      • Ruth F. Curtain

      Pages 45-51

   4. An Introduction to Nonlinear Filtering

      • M. H. A. Davis, Steven I. Marcus

      Pages 53-75

   5. A Tutorial Introduction to Differentiable Manifolds and Vector Fields

      • Michiel Hazewinkel

      Pages 77-93

   6. A Short Tutorial on Lie Algebras

      • Michiel Hazewinkel

      Pages 95-108

4. Foundations of Stochastic Systems and Modeling Issues and Applications

   1. Front Matter

      Pages 109-109

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   2. Mathematical Models of Chemical Reactions

      • Ludwig Arnold

      Pages 111-134

   3. Qualitative Theory of Real Noise Excited Systems

      • Ludwig Arnold

      Pages 135-140

   4. Stochastic Models of Computer Networks

      • René Boel

      Pages 141-167

   5. State Space Models for Gaussian Stochastic Processes

      • Anders Lindquist, Giorgio Picci

      Pages 169-204

   6. Ergodic Theory of Linear Parameter-Excited Systems

      • Volker Wihstutz

      Pages 205-218

5. Identification

   1. Front Matter

      Pages 219-219

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   2. System Identification

      • E. J. Hannan

      Pages 221-246

   3. Recursive Identification

      • Lennart Ljung

      Pages 247-281

   4. The Properties of the Parameterization of ARMAX Systems in Structural Specification and their Relevance for Estimation

      • M. Deistler

      Pages 283-289

   5. Tests of Adequacy for Arma Models and Tests of Separated Hypotheses

      • Guégan Dominique

      Pages 291-297

In the last five years or so there has been an important renaissance in the area of (mathematical) modeling, identification and (stochastic) control. It was the purpose of the Advanced Study Institute of which the present volume constitutes the proceedings to review recent developments in this area with par­ ticular emphasis on identification and filtering and to do so in such a manner that the material is accessible to a wide variety of both embryo scientists and the various breeds of established researchers to whom identification, filtering, etc. are important (such as control engineers, time series analysts, econometricians, probabilists, mathematical geologists, and various kinds of pure and applied mathematicians; all of these were represented at the ASI). For these proceedings we have taken particular care to see to it that the material presented will be understandable for a quite diverse audience. To that end we have added a fifth tutorial section (besides the four presented at the meeting) and have also included an extensive introduction which explains in detail the main problem areas and themes of these proceedings and which outlines how the various contributions fit together to form a coherent, integrated whole. The prerequisites needed to understand the material in this volume are modest and most graduate students in e. g. mathematical systems theory, applied mathematics, econo­ metrics or control engineering will qualify.

• Ergodic theory
• Stochastic calculus
• Stochastic processes
• Variance
• diffusion process
• filtering problem
• stochastic process

• Erasmus Universiteit, Rotterdam, The Netherlands

  Michiel Hazewinkel

• Rijksuniversiteit, Groningen, The Netherlands

  Jan C. Willems

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