@article{AIHPB_1980__16_3_225_0, author = {Ruckebusch, Guy}, title = {Th\'eorie g\'eom\'etrique de la {Repr\'esentation} {Markovienne}}, journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques}, pages = {225--297}, publisher = {Gauthier-Villars}, volume = {16}, number = {3}, year = {1980}, mrnumber = {595201}, zbl = {0441.60072}, language = {fr}, url = {http://www.numdam.org/item/AIHPB_1980__16_3_225_0/} }
TY - JOUR AU - Ruckebusch, Guy TI - Théorie géométrique de la Représentation Markovienne JO - Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques PY - 1980 SP - 225 EP - 297 VL - 16 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPB_1980__16_3_225_0/ LA - fr ID - AIHPB_1980__16_3_225_0 ER -
%0 Journal Article %A Ruckebusch, Guy %T Théorie géométrique de la Représentation Markovienne %J Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques %D 1980 %P 225-297 %V 16 %N 3 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPB_1980__16_3_225_0/ %G fr %F AIHPB_1980__16_3_225_0
Ruckebusch, Guy. Théorie géométrique de la Représentation Markovienne. Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 16 (1980) no. 3, pp. 225-297. http://www.numdam.org/item/AIHPB_1980__16_3_225_0/
[Aka-1] Stochastic theory of minimal realizations. I. E. E. E. Trans. Automatic Control, AC-19, 1974, p. 667-674. | MR | Zbl
,[Aka-2] Markovian representation of stochastic processes by canonical variables. S. I. A. M. J. Control., t. 13, 1975, p. 162-173. | MR | Zbl
,[And] The inverse problem of stationary covariance generation J. Statistical Physics, t. 1, 1969, p. 133-147. | MR
,[AnK] Forwards, backwards and dynamically reversible Markovian models of second order processes. Proc. 1978 I. E. E. E. International Symposium on Circuits and Systems, New York, p. 981-986. | MR
et ,[AnV] Network analysis and synthesis. A modern System Theory approach, Prentice-Hall, New Jersey, 1973.
et ,[BaB] H2-functions and infinite dimensional realization theory. S. I. A. M. J. Control, t. 13, 1975, p. 221-241. | MR | Zbl
et ,[BaD] Invariant subspace methods in linear multivariable-distributed systems and lumped-distributed network synthesis. Proc. I. E. E. E., t. 64, 1976, p. 160-178. | MR
et ,[BBF] State-space model for infinite dimensional systems. I. E. E.E. Trans. Automatic Control, AC-19,1974, p.693-700. | MR | Zbl
, et ,[Ben] Filtrage optimal des systèmes linéaires, Dunod, Paris, 1971. | Zbl
,[Bir] Lattice theory. Amer. Math. Soc., Coll. Publ., vol. 25, Providence, Rhode Island, 1948. | MR | Zbl
,[B1G] Markov processes and potential theory, Academic Press, New York, 1968. | MR | Zbl
et ,[BoJ] Time series analysis: forecasting and control, Holden Day, San Francisco, 1976. | MR | Zbl
et ,[Bro] Finite dimensional linear systems, J. Wiley and Sons, New York, 1970. | Zbl
,[Cas] Dynamical systems and their applications: Linear theory. Mathematics in Science and Engineering, vol. 135, Academic Press, New York, 1977. | MR | Zbl
,[Che] Introduction to linear system theory. H. R. W. Series in Electrical Engineering, Electronics and Systems, Holt, Rinehart and Winston, 1970.
,[CuP] Infinite dimensional linear systems theory. Lecture notes in Control and Information Science, vol. 8, Springer-Verlag, Berlin, 1978. | MR | Zbl
et ,[Dav] Factoring the spectral matrix. I. E. E. E. Trans. Automatic Control, AC-8, 1963, p. 296-305.
,[Doo-1] The elementary Gaussian processes. Annals of Math. Stat., t. 15, 1944, p. 229-282. | MR | Zbl
,[Doo-2] Stochastic processes, J. Wiley and Sons, New York, 1953. | MR | Zbl
,[DSS] Cyclic vectors and invariant subspaces for the backward shift operator. Ann. Inst. Fourier (Grenoble), t. 20, 1970, p. 37-76. | Numdam | MR | Zbl
, et ,[Dun] A geometric approach to linear control and estimation (à paraître).
,[DuS] Linear operators, vol. 1, Interscience, New York, 1957. | Zbl
et ,[DyM] Gaussian processes, function theory and the inverse spectral problem, Academic Press, New York, 1976. | MR | Zbl
et ,[Fau-1] Representation of stochastic processes, Ph. D. Dissertation, Stanford University, February 1967.
,[Fau-2] Réalisations Markoviennes de processus stationnaires. Rapport de recherche, n° 13, 1973, I. R. I. A., 78150 Le Chesnay.
,[FCG] Opérateurs rationnels positifs. Application à l'hyperstabilité et aux processus aléatoires. Méthodes Mathématiques de l'informatique, t. 8, Dunod, Paris, 1979. | MR | Zbl
, et ,[Fuh-1] Realization theory in Hilbert space for a class of transfer functions. J. Funct. Anal., t. 18, 1975, p. 338-349. | MR | Zbl
,[Fuh-2] Exact controllability and observability and realization theory in Hilbert space. J. of Math. Anal. and applications, t. 53, 1976, p. 377-392. | MR | Zbl
,[Fuh-3] Linear operators and systems in Hilbert space (à paraître), McGraw-Hill. | Zbl
,[Ger] Algorithmes de calcul de réalisations Markoviennes. Cas singuliers et stabilité. Rapport de recherche, n° 66, 1973, I. R. I. A., 78150 Le Chesnay.
,[Hal] Shifts on Hilbert spaces. J. Reine Angew. Math., t. 208, 1961, p. 102-112. | MR | Zbl
,[Han] Multiple time series, Wiley and Sons, New York, 1970. | MR | Zbl
,[Hel-1] Lectures on invariant subspaces, Academic Press, New York, 1964. | MR | Zbl
,[Hel-2] Discrete time systems, operator models and scattering theory. J. Funct. Anal., t. 16, 1974, p. 15-38. | MR | Zbl
,[Hel-3] Systems with infinite-dimensional state space : the Hilbert space approach. Proc. I. E. E. E., t. 64, 1976, p. 145-160. | MR
,[Hof] Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. | MR | Zbl
,[IbR] Processus aléatoires Gaussiens, Éditions de Moscou, 1974. | Zbl
et ,[Kai] A view of three decades of linear filtering theory. I. E. E. E. Trans. Info. Theory, IT-20, vol. 2, 1974, p. 146-181. | MR | Zbl
,[KaG] An innovations approach to least-squares estimation. Part IV: Recursive estimation given lumped covariance functions. I. E. E. E. Trans. Automatic Control, AC-16, 1971, p. 720-727. | MR
et ,[KMS] Some new algorithms for recursive estimation in constant discrete-time linear systems. Proc. seventh Princeton Symp. on Information and system science, 1973, p. 344-352.
, et ,[Kal-1] A new approach to linear filtering and prediction problems. Trans. Amer. Soc. Mech. Eng., J. Basic Engineering, t. 82, 1960, p. 35-45.
,[Kal-2] Linear stochastic filtering. Reappraisal and outlook. Proc. Symposium on System Theory, Polytechnic Institute of Brooklyn, 1965, p. 197-205. | MR
,[Kal-3] Lectures on controllability and observability. C. I. M. E. Summer course 1968, Cremonese, Roma, 1969, p. 1-149. | MR | Zbl
,[KFA] Topics in Mathematical System Theory, McGraw-Hill, New York, 1969. | MR | Zbl
, et ,[Kat] Perturbation theory for linear operators, Springer-Verlag, New York, 1966. | MR | Zbl
,[Kol] Stationary sequences in Hilbert space (en russe). Bull. Math. Univ. Moscou, vol. 2, n° 6, 1941, p. 1-40. | MR | Zbl
,[LaP] Scattering theory, Academic Press, New York, 1967. | MR | Zbl
et ,[Lin] A new algorithm for optimal filtering of discrete-time stationary processes. S. I. A. M. J. Control, t. 12, 1974, p. 736-746. | MR | Zbl
,[LiP-1] On the stochastic realization problem. S. I. A. M. J. Control (à paraître). | Zbl
et ,[LiP-2] On the structure of minimal splitting subspaces in stochastic realization theory. Proc. 1977 Conf. Decision and Control,New Orleans, 1977, p. 42-48. | MR
et ,[LiP-3] A state-space theory for stationary stochastic processes. Proc. 21st Midwest Symposium on Circuits and Systems, Ames, Iowa, August 1978.
et ,[LiP-4] A Hardy space approach to the stochastic realization problem. Proc. 1978 Conf. Decision and Control, San Diego, January 1979. | MR | Zbl
et ,[LiP-5] Realization theory for multivariate stationary Gaussian processes I: State space construction. 4th Int. Symposium on the Mathematical theory of Networks and Systems, Delft (Pays-Bas), 1979, p. 140-148. | Zbl
et ,[LPR] On minimal splitting subspaces and Markovian representations. Mathematical Systems Theory, t. 12, 1979, p. 271-279. | MR | Zbl
, et ,[LjK] Backwards Markovian models for second-order stochastic processes. I. E. E. E. Trans. Info. Theory, IT-22, 1976, p. 488-491. | MR | Zbl
et ,[Man] On multivariate wide-sense Markovprocesses. Nagoya Math. J., vol. 33, 1968, p. 7-19. | MR | Zbl
,[Mas] On helixes in Hilbert space I. Theory of Proba. and its applications, vol. 17, 1972, p. 1-19. | MR | Zbl
,[MaR] The time-domain of continuous parameter weakly stationary stochastic processes. Pacific J. Math., t. 12, 1962, p. 1361-1378. | MR | Zbl
et ,[MeL] Systems identification: advances and case studies, Academic Press, New York, 1977.
et ,[MeP] Stochastic Integration, Academic Press, à paraître. | Zbl
et ,[Mey] Processus de Markov, Springer-Verlag, Berlin, 1967. | MR | Zbl
,[Nev-1] Processus aléatoires Gaussiens, Presses de l'Université de Montréal, 1968. | MR | Zbl
,[Nev-2] Intégrales stochastiques et applications, Cours de 3e cycle, Université de Paris VI, 1971-1972.
,[Pic] Stochastic realization of Gaussian processes. Proc. I. E. E. E., t. 64, 1976, p. 112-122. | MR
,[Pot] The multiplicative structure of J contractive matrix functions. Amer. Math. Soc. Transl., t. 15, 1960, p. 131-243. | MR | Zbl
,[RiS] Leçons d'analyse fonctionnelle, Gauthier-Villars, Paris, 1965. | Zbl
et ,[Roz-1] Stationary random processes, Holden Day, San Francisco, 1967. | MR | Zbl
,[Roz-2] On two selected topics connected with Stochastic System Theory. Applied Math. and Optimization, vol. 3, n° 1, 1976, p. 73-80. | MR | Zbl
,[Roz-3] On Markov extensions of a random process. Theory of Proba. and its applications, vol. 22, 1977, p. 190-195. | Zbl
,[Ruc-1] Représentations Markoviennes de processus Gaussiens stationnaires. Thèse de 3e cycle, Lab. de Calcul des Probabilités, Université de Paris VI, mai 1975.
,[Ruc-2] Représentations Markoviennes de processus Gaussiens stationnaires. C. R. Acad. Sciences, Paris, Série A, t. 282, 1976, p. 649-651. | MR | Zbl
,[Ruc-3] Représentations Markoviennes de processus Gaussiens stationnaires et applications statistiques. Journées de Statistique des processus stochastiques, Grenoble, 1977, Springer-Verlag, Berlin, Lecture Notes in Mathematics, t. 636, p. 115-139. | Zbl
,[Ruc-4] On the theory of Markovian Representation. Proc. Measure theory-applications to stochastic analysis, Oberwolfach (Allemagne), 1977, Springer-Verlag, Berlin, Lecture Notes in Mathematics, t. 695, p. 77-87. | MR | Zbl
,[Ruc-5] A state space approach to the stochastic realization problem. Proc. 1978 I. E. E. E. International Symposium on Circuits and Systems, New York, p. 972-977.
,[Ruc-6] Factorisations minimales de densités spectrales et représentations Markoviennes. Proc. 1er Colloque A. F. C. E. T.-S. M. F. de Mathématiques Appliquées, t. I, École Polytechnique, 91128 Palaiseau, 1978, p. 365-375. | Zbl
,[Ruc-7] A geometric approach to the stochastic realization problem. Rapport interne, n° 41, Centre de Math. Appliquées, École Polytechnique, 91128 Palaiseau, novembre 1978, soumis à publication.
,[Ruc-8] Observability and constructibility in the theory of Markovian representation. 4th Int. Symposium on the Mathematical theory of Networks and Systems, Delft (Pays-Bas), 1979, p. 128-132. | Zbl
,[Ruc-9) Théorie géométrique de la Représentation Markovienne. Thèse d'État, Lab. de Calcul des Probabilités, Université de Paris VI, avril 1980.
,[Sal] Identification optimale des systèmes linéaires stochastiques. Thèse d'État, Université Paul-Sabatier, Toulouse, 1976.
,[SzF-1] Opérateurs sans multiplicité. Acta Sci. Math., t. 30, 1969, p. 1-18. | MR | Zbl
et ,[SzF-2] Harmonic analysis of operators on Hilbert space, North Holland, Amsterdam, 1970. | MR | Zbl
et ,[Tay] Introduction to functional analysis, John Wiley and Sons, New York, 1958. | MR | Zbl
,[Urb] Lectures on Prediction Theory, Springer-Verlag, New York, 1967. | MR | Zbl
,[VaV] On stochastic dynamical systems. 4th Int. Symposium on the Mathematical Theory of Networks and Systems, Delft (Pays-Bas), 1979, p. 350-356. | Zbl
et ,[WiM] The prediction theory of multivariate stochastic processes, Part I. Acta Math., t. 98, 1957, p. 111-150; Part II, Acta Math., t. 99, 1958, p. 93-137. | Zbl
et ,[Wil-1] Least squares stationary optimal control and the algebraic Riccati equation. I. E. E. E. Trans. Automatic Control, AC-16, 1971, p. 621-634. | MR
,[Wil-2] Dissipative dynamical systems, Part II: Linear systems with quadratic supply rates. Archive for rational Mechanics and Analysis, t. 45, 1972, p. 352-393. | MR | Zbl
,[WiV] Stochastic systems and the problem of state space realization (à paraître).
et ,[Wol] A study in the analysis of stationary time series, Almquist and Wiksell, Stockholm, 1938. | JFM | MR | Zbl
,[Won] Linear multivariable control. A geometric approach, Springer-Verlag, Berlin, Lecture Notes in Economics and Mathematical Systems, t. 101, 1974. | MR | Zbl
,[Yos] Functional analysis, Springer-Verlag, Berlin, 1974. | MR | Zbl
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