This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Balakrishnan, Applied Functional Analysis. Springer Verlag, 1976.
A. Bensoussan, Filtrage Optimal des Systemes Lineaires, Dunod, 1971.
A. Bensoussan, Control of Stochastic Partial Differential Equations, p. 209–245, "Distributed Parameter Systems: Identification, Estimation and Control", Ed. W.H. Ray and F.G, Lainiotis, 1978. Marcel Dekker.
J.G. Borisovic, and A.S. Turbabin, On the Cauchy Problem for Linear Non-homogeneous differential equations with retarded arguments. Soviet Math. Dokl., 10(1969), p. 401–405.
A. Chojnowska-Michalik, Stochastic Differential Equations in Hilbert Spaces and their Applocations. Ph. D. Thesis, Institute of Mathematics Polish Academy of Sciences, 1976.
R.F. Curtain, and P.L. Falb, Itô's Lemma in Infinite Dimensions. J. Math. Anal. and Appl., 1970, Vol. 31, p. 434–448.
R.F. Curtain and P.L. Falb, Stochastic Differential Equations in Hilbert Space, J. Diff. Eqns. 10(1971) p. 412–430.
R.F. Curtain, Stochastic Evolution Equations with General White Noise Disturbance. J. Math. Anal. and Appl. 1977, 60 p. 570–595.
R.F. Curtain, and A.J. Pritchard, A Semigroup Approach to Infinite Dimensional Systems Theory. Proc. IMA Conf. ‘Recent Developments in Control', Leicester, U.K. 1976.
R.F. Curtain, Estimation and Stochastic Control for Linear Infinite Dimensional Systems," p. 45–56 "Probabilistic Analysis and Related Topics", Volume 1, 1978, Academic Press.
R.F. Curtain and A.J. Pritchard, Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences. Vol. 8, 1978, Springer Verlag.
R.F. Curtain, A semigroup Approach to the LQG Problem for Infinite Dimensional Systems, Proc. IEEE, 1978.
R.F. Curtain, Mathematical Models for Random Vibration Problems. International Symposium of the Analysis and Optimization of Stochastic Systems, Oxford, U.K., 1978.
R.F. Curtain, Asymptotic Stability of Second Order Linear Stochastic Partial Differential Equations, 1978 (Submitted to SIAM J. Applied Mathematics).
R.F. Curtain, and A.J. Pritchard, An Abstract Theory for Unbounded Control Action for Distributed Parameter Systems. SIAM J. Control 15, pp. 566–611.
R.F. Curtain, Linear Stochastic Control for Distributed Systems with Boundary Control, Boundary Noise and Point Observations. Control Theory Centre Report No. 46, 1976, University of Warwick, Coventry, England.
M.C. Delfour, and S.K. Mitter, Hereditary Differential Systems with Constant. Delays I: General case, J. Diff. Eqns. 12 (1972) p. 213–235.
U.G. Haussmann, Asymptotic Stability of the Linear Itô Equation in Infinite Dimensions. J. Math. Anal. and Appl. 65 (1978) p. 219–235.
E. Hille, and R.S. Phillips, Functional Analysis and Semigroups. Colloq. Amer. Math. Soc. 31, 1957.
A. Ichikawa, Linear Stochastic Evolution Equations in Hilbert Space. Control Theory Centre Report No. 51. University of Warwick, 1976 (To appear in J. Diff. Eqns).
A. Ichikawa, Dynamic Programming Approach to Stochastic Evolution Equations. Control Theory Centre Report No. 60. University of Warwick, 1977. (To appear in SIAM J. Control + Opt., 1979).
M. Metivier, Integrale Stochastique par rapport a des processus a valeurs dans un espace de Banach relexif. The Prob. and Appl. Tom. 19, 1974.
M. Metivier, and G. Pistone, Une formule d'isometrie pour l'integrale stochastique hilbertienne et equations d'evolution lineaires stochastiques. Z. Wahrschein. 33 (1975) p. 1–18.
E. Pardoux, Doctoral Thesis, L"Université de Paris Sud, Centre d'Orsay, 1978.
A.J. Pritchard, and J. Zabczyk, Stabilizibility of Infinite Dimensional Systems. Control Theory Centre Report, University of Warwick, U.K., No. 70, 1977.
M. Slemrod, Asymptotic Behaviour of Co Semigroup as Determined by the Spectrum of the generator, Indiana, J. 25 (1976) pp. 783–792.
R. Vinter, A Representation of Solutions to Stochastic Delay Equations. Imperial College of Science and Technology. Dept. of Computing and Control Report, 1975.
R. Vinter, Semigroup on Product Spaces and Applications to Initial Value Problems with Nonlocal Boundary Conditions. Proc. 2nd IFAC Symposium on the Control of Distributed Parameter Systems. University of Warwick, 1975.
J. Zabczyk, A semigroup Approach to Boundary Value Control. Ibid.
J. Zabczyk, On Stability of Infinite Dimensional Linear Stochastic Systems. Proc. Banach Centre. Prob. Semester, Warsaw, 1976.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Curtain, R.F. (1979). Linear stochastic itô equations in Hilbert space. In: Kohlmann, M., Vogel, W. (eds) Stochastic Control Theory and Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009376
Download citation
DOI: https://doi.org/10.1007/BFb0009376
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09480-7
Online ISBN: 978-3-540-35211-2
eBook Packages: Springer Book Archive