Linear Stochastic Systems

• 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

"The purpose of this book is to present the mathematical background necessary for understanding the linear state-space modeling of second-order random processes and its applications to estimation and identification theory. ... this monograph is an excellent reference for researchers interested in geometric theory of stochastic realization and its applications." (Viorica M. Ungureanu, Mathematical Reviews, January, 2016)