Linear stochastic itô equations in Hilbert space

  • Ruth F. Curtain
Part I: Survey Lectures
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)


Hilbert Space Strong Solution Wiener Process Mild Solution Continuous Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.V. Balakrishnan, Applied Functional Analysis. Springer Verlag, 1976.Google Scholar
  2. 2.
    A. Bensoussan, Filtrage Optimal des Systemes Lineaires, Dunod, 1971.Google Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    A. Chojnowska-Michalik, Stochastic Differential Equations in Hilbert Spaces and their Applocations. Ph. D. Thesis, Institute of Mathematics Polish Academy of Sciences, 1976.Google Scholar
  6. 6.
    R.F. Curtain, and P.L. Falb, Itô's Lemma in Infinite Dimensions. J. Math. Anal. and Appl., 1970, Vol. 31, p. 434–448.Google Scholar
  7. 7.
    R.F. Curtain and P.L. Falb, Stochastic Differential Equations in Hilbert Space, J. Diff. Eqns. 10(1971) p. 412–430.Google Scholar
  8. 8.
    R.F. Curtain, Stochastic Evolution Equations with General White Noise Disturbance. J. Math. Anal. and Appl. 1977, 60 p. 570–595.Google Scholar
  9. 9.
    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.Google Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    R.F. Curtain and A.J. Pritchard, Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences. Vol. 8, 1978, Springer Verlag.Google Scholar
  12. 12.
    R.F. Curtain, A semigroup Approach to the LQG Problem for Infinite Dimensional Systems, Proc. IEEE, 1978.Google Scholar
  13. 13.
    R.F. Curtain, Mathematical Models for Random Vibration Problems. International Symposium of the Analysis and Optimization of Stochastic Systems, Oxford, U.K., 1978.Google Scholar
  14. 14.
    R.F. Curtain, Asymptotic Stability of Second Order Linear Stochastic Partial Differential Equations, 1978 (Submitted to SIAM J. Applied Mathematics).Google Scholar
  15. 15.
    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.Google Scholar
  16. 16.
    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.Google Scholar
  17. 17.
    M.C. Delfour, and S.K. Mitter, Hereditary Differential Systems with Constant. Delays I: General case, J. Diff. Eqns. 12 (1972) p. 213–235.Google Scholar
  18. 18.
    U.G. Haussmann, Asymptotic Stability of the Linear Itô Equation in Infinite Dimensions. J. Math. Anal. and Appl. 65 (1978) p. 219–235.Google Scholar
  19. 19.
    E. Hille, and R.S. Phillips, Functional Analysis and Semigroups. Colloq. Amer. Math. Soc. 31, 1957.Google Scholar
  20. 20.
    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).Google Scholar
  21. 21.
    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).Google Scholar
  22. 22.
    M. Metivier, Integrale Stochastique par rapport a des processus a valeurs dans un espace de Banach relexif. The Prob. and Appl. Tom. 19, 1974.Google Scholar
  23. 23.
    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.Google Scholar
  24. 24.
    E. Pardoux, Doctoral Thesis, L"Université de Paris Sud, Centre d'Orsay, 1978.Google Scholar
  25. 25.
    A.J. Pritchard, and J. Zabczyk, Stabilizibility of Infinite Dimensional Systems. Control Theory Centre Report, University of Warwick, U.K., No. 70, 1977.Google Scholar
  26. 26.
    M. Slemrod, Asymptotic Behaviour of Co Semigroup as Determined by the Spectrum of the generator, Indiana, J. 25 (1976) pp. 783–792.Google Scholar
  27. 27.
    R. Vinter, A Representation of Solutions to Stochastic Delay Equations. Imperial College of Science and Technology. Dept. of Computing and Control Report, 1975.Google Scholar
  28. 28.
    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.Google Scholar
  29. 29.
    J. Zabczyk, A semigroup Approach to Boundary Value Control. Ibid.Google Scholar
  30. 30.
    J. Zabczyk, On Stability of Infinite Dimensional Linear Stochastic Systems. Proc. Banach Centre. Prob. Semester, Warsaw, 1976.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Ruth F. Curtain
    • 1
  1. 1.Mathematics InstituteUniversity of GroningenThe Netherlands

Personalised recommendations