Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification

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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