Markovian Representation of Stochastic Processes by Canonical Variables
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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.
Estimation and detection in stochastic control theory, Stationary stochastic processes, Signal detection and filtering (aspects of stochastic processes)
Estimation and detection in stochastic control theory, Stationary stochastic processes, Signal detection and filtering (aspects of stochastic processes)
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