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Markovian Representation of Stochastic Processes by Canonical Variables
Abstract
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.
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Citations
Cited by
Verhaegen, M. (1994) · Automatica · doi:10.1016/0005-1098(94)90229-1 · Cited by 961
Canonical variate analysis in identification, filtering, and adaptive control
Larimore, W. E. (1990) · 29th IEEE Conference on Decision and Control · doi:10.1109/cdc.1990.203665 · Cited by 573
Subspace-based fault detection algorithms for vibration monitoring
Basseville, M., Abdelghani, M., & Benveniste, A. (2000) · Automatica · doi:10.1016/s0005-1098(99)00093-x · Cited by 296
Realization theory for multivariate stationary Gaussian processes
Lindquist, A., & Picci, G. (1985) · SIAM Journal on Control and Optimization · doi:10.1137/0323050 · Cited by 139
Metadata
- Authors
- Akaike, H.
- Venue
- SIAM Journal on Control
- Published
- 1975-01
- Volume
- 13
- Issue
- 1
- Pages
- 162-173
- ISSN
- 0036-1402 (ISSN-L)
- OpenAlex
- W1986803336
- Cited by
- 357
- References
- 0
- FWCI
- 13.52
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Markovian Representation of Stochastic Processes by Canonical Variables. https://app.cochat.ai/papers/10.1137/0313010
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- Akaike, H. (1975). Markovian Representation of Stochastic Processes by Canonical Variables. SIAM Journal on Control. https://doi.org/10.1137/0313010
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