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