On the nonlinear stochastic realization problem

References

• Arveson , W. 1986 . Markov operators and O.S.-Positive process . J. Funct. Anal , 66 : 173 – 234 .
   Web of Science ®Google Scholar
• Badawi , F. , Lindquist , A. and Pavon , M. 1979 . A stochastic realization approach to the smoothing problem . IEEE Trans Automat. Control , 24 : 878 – 888 .
   Web of Science ®Google Scholar
• Blumenthal , R. M. and Getoor , R. K. 1986 . Markov Processes and Potential Theory , New York : Academic Press .
   Google Scholar
• Hida , T. 1980 . “ Brownian Motion ” . In Applications in Mathematics Series , New York : Springer-Verlag . #11
   Google Scholar
• Ionescu-Tulcea , A. and Ionescu-Tulcea , G. 1969 . Topics in the Theory of Lifting , New York : Springer-Verlag .
   Google Scholar
• Kalman , R. E. Linear stochastic filtering-reappraisal and outlook . Proc. Symp. System Theory, Polytechnic Inst, of Brooklyn . pp. 197 – 205 .
   Google Scholar
• Klein , A. 1978 . The semigroup characterization of Osterwolder-Schrader path spaces and the construction of Euclidean fields . J. Func. Anal. , 27 : 277 – 291 .
   Google Scholar
• Lax , P. D. , Phillips , R. S. , Lindquist , A. , Pavon , M. and Picci , G. 1967 . “ Recent trends in stochastic realization theory ” . In Prediction Theory and Harmonic Analysis: The Pesi Masani Volume , Edited by: Mandrekar , V. and Salehi , H. New York : Academic Press .
   Google Scholar
• Lindquist , A. , Mitter , S. and Picci , G. 1982 . “ Toward a theory of nonlinear stochastic realization ” . In Feedback and Synthesis of Linear and Nonlinear Systems , Edited by: Hinrichsen , D. and Isidori , A. 175 – 189 . Springer-Verlag .
   Google Scholar
• Lindquist , A. and Picci , G. 1985 . Realization theory for multivariate stationary Gaussian processes . SIAM J. Control and Optimization , 23 : 809 – 857 .
   Web of Science ®Google Scholar
• Lindquist , A. and Picci , G. 1985 . “ Realization theory for multivariate stationary Gaussian processes ” . In SIAM J. Control and Optimization Vol. 23 , 809 – 857 .
   Google Scholar
• Mc Kean , H. P. 1963 . Brownian motion with several dimensional time . Theory Prob, App , VIII : 335 – 354 .
   Google Scholar
• Meyer , P. A. 1976 . Probability and Potentials , Waltham, Massachusetts : Baisdell Publishing Co. .
   Google Scholar
• Moore , R. T. 1968 . “ Measurable, continuous and smooth vectors for semigroups and groups representations ” . In Mem. of the AMS V 78 – 78 .
   Google Scholar
• Nelson , E. 1958 . The adjoint Markov process . Duke Math. J. , 25 : 671 – 690 .
   Google Scholar
• Nelson , E. 1959 . Regular probability measures on function space . Annals of Math. , 69 : 630 – 643 .
   Web of Science ®Google Scholar
• Pavon , M. 1984 . New results in the interpolation problem for continuous time stationary increment process . SIAM J. Control Optim. , 22 : 133 – 142 .
   Google Scholar
• Picci , G. 1986 . “ Application of stochastic realization theory to a fundamental problem of physics ” . In Modelling, Identification and Robust Control , Edited by: Byrnes , C. I. and Lindquist , A. North Holland : Elsevier Science Publishers B.V .
   Google Scholar
• Ruckebusch , G. 1980 . Théorie géométrique de la représentation Markovienne . Ann. Inst. H. PoincaréXVI , B : 225 – 297 .
   Google Scholar
• Shiryayev , A. N. 1984 . Probability , New York : Springer-Verlag .
   Google Scholar
• Sinai , G. Ja. 1964 . Dynamical systems with countably-multiple Lebesgue spectrum. I . AMS Transl. , 2 ( 39 ) : 83 – 110 .
   Google Scholar
• Takesaki , M. 1979 . Theory of Operator Algebras. I , New York : Springer-Verlag .
   Google Scholar
• Van Casteren , J. A. 1984 . Generators of strongly continuous semigroups , Vol. 115 , Boston : Pitman Advanced Publishing .
   Google Scholar
• Van Putter , C. and Van Schuppen , J. H. 1985 . Invariance properties of the conditional independence relation . Annals of Probability , 13 : 934 – 945 .
   Google Scholar
• Van Schuppen , J. H. 1982 . “ The strong finite stochastic realization problem-preliminary results ” . In Proceedings of the Fifth lnrernulional Conference on Analysis and Optimization of Systems , Edited by: Bensoussan , A. and Lions , J. L. Vol. 44 , Springer-Verlag Lecture Notes on Control and Information .
   Google Scholar
• Lindquist , A. and Picci , G. 1985 . Forward and backward semimartingale models for Gaussian processes with stationary increments . Stochastics , 15 : 1 – 50 .
   Google Scholar
• Lipster , R. S. and Shiryayev , A. N. 1977 . Statistics of Random Processes , New York : Springer-Verlag .
   Google Scholar
• Fleming , W. and Rishel , R. 1975 . Deterministic and Stochastic Optimal Control , New York : Springer-Verlag .
   Google Scholar
• Taylor , T. J. S. and Pavon , M. 1988 . A solution of the nonlinear stochastic realization problem . Systems and Control Letters , 11 : 117 – 121 .
   Google Scholar
• Dunford , N. and Schwartz , J. T. 1963 . Linear operators , Vol. Part II , New York : Wiley Interscience .
   Google Scholar
• Taylor , T. J. S. Contributions to the theory of nonlinear stochastic realization, to be published
   Google Scholar
• Van Putten , C. and Van Schuppen , J. H. On stochastic dynamical systems . Proc. 4th MTNS Conf . Delft, Netherlands. pp. 350 – 356 .
   Google Scholar