1975/01/01 by Hirotugu Akaike · 1 citation
Computer Science · Physics and Astronomy · Mathematics · #Neural Networks and Applications #Chaos control and synchronization #Statistical Mechanics and Entropy #Realization (probability) #Mathematics #Canonical correlation #Canonical form #Stochastic process #Extension (predicate logic) #Representation (politics) #Markov process #Continuous-time stochastic process #Probabilistic logic #Interpretation (philosophy) #Kalman filter #Applied mathematics #Computer science #Pure mathematics #Statistics
paper · doi:10.1137/0313010
openalex publication_date 1975/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
The structure of the information interface between the future and the past of a discrete-time stochastic process is analyzed by using the concepts of canonical correlation analysis. Two extreme Markovian representations are obtained with states defined by the sets of canonical variables which represent the past information projected on the future and the future information projected on the past, respectively. The result completely clarifies the probabilistic structure of the Faurre algorithm of realization of stochastic systems. By an extension of the basic result the Ho–Kalman algorithm of realization of general systems is also given a stochastic interpretation.