Stochastic Systems: The Mathematics of Filtering and Identification and Applications

Table of Contents

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   Book Overview
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   Chapter 1 Introduction: An Annotated Navigation Chart and Sketch of the Main Themes in this Volume and their Interrelations
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   Chapter 2 The LQG-Problem: A Brief Tutorial Exposition
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   Chapter 3 A Tutorial Article on the Itô Integral and the Stochastic Calculus
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   Chapter 4 An Introduction to Nonlinear Filtering
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   Chapter 5 A Tutorial Introduction to Differentiable Manifolds and Vector Fields
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   Chapter 6 A Short Tutorial on Lie Algebras
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   Chapter 7 Mathematical Models of Chemical Reactions
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   Chapter 8 Qualitative Theory of Real Noise Excited Systems
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    Chapter 9 Stochastic Models of Computer Networks
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    Chapter 10 State Space Models for Gaussian Stochastic Processes
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    Chapter 11 Ergodic Theory of Linear Parameter-Excited Systems
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    Chapter 12 System Identification
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    Chapter 13 Recursive Identification
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    Chapter 14 The Properties of the Parameterization of ARMAX Systems in Structural Specification and their Relevance for Estimation
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    Chapter 15 Tests of Adequacy for Arma Models and Tests of Separated Hypotheses
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    Chapter 16 Some Nonlinear Filtering Problems Arising in Recursive Identification
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    Chapter 17 Some Topics in Linear Estimation
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    Chapter 18 Inverse Scattering and Linear Prediction, the Time Continuous Case
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    Chapter 19 Harmonic Analysis and the Mathematics Behind Filtering and Prediction (D’Apres Cartier D’Apres Wiener and Kolmogorov)
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    Chapter 20 Deterministic and Stochastic Model Reference Adaptive Control
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    Chapter 21 Adaptive Control of Systems Subject to a Class of Random Parameter Variations and Disturbances
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    Chapter 22 On Stochastic Self-Tuning Methods
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    Chapter 23 Nonlinear Systems and Nonlinear Estimation Theory
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    Chapter 24 Non-Linear Filtering and Stochastic Mechanics
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    Chapter 25 Pathwise Non-Linear Filtering
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    Chapter 26 Non-linear Filtering, Prediction and Smoothing
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    Chapter 27 Estimation Problems with Low Dimensional Filters
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    Chapter 28 Group Invariance Methods in Nonlinear Filtering of Diffusion Processes
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    Chapter 29 Asymptotic Bounds on the Minimal Error of Non-Linear Filtering
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    Chapter 30 An Approximation to Optimal Nonlinear Filtering with Discontinuous Observations
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    Chapter 31 Some Results and Speculations on the Role of Lie Algebras in Filtering
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    Chapter 32 Deterministic Estimation and Asymptotic Stochastic Estimation
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    Chapter 33 Non-Linear Filtering Equation and a Problem of Parametric Estimation
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    Chapter 34 Regularity of Conditional Laws in Non-Linear Filtering Theory and Stochastic Calculus of Variations
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    Chapter 35 Finite Dimensional Estimation Algebras in Nonlinear Filtering
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    Chapter 36 Rigorous Results on the Cubic Sensor Problem
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    Chapter 37 A Footnote to the Papers which Prove the Nonexistence of Finite Dimensional Filters