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Some results on bellman equation in Hilbert spaces and applications to infinite dimensional control problems

  • G. Da Prato
Control Theory
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 69)

Keywords

Hilbert Space Bellman Equation Stochastic Control Problem Stochastic Evolution Equation Complete Orthonormal System 
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References

  1. [1]
    V. BARBU, G. Da PRATO, Hamilton Jacobi Equations in Hilbert Spaces, PITMAN, London (1983).Google Scholar
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    V. BARBU, G. Da PRATO, Solution of the Bellman Equation Associated with an Infinite Dimensional Stochastic Control Problem and Synthesis of Optimal Control, SIAM J. Control and Optimization, 21, 4 (1983 531–550.Google Scholar
  3. [3]
    G. DA PRATO, Some Results on Bellman Equation in Hilbert Spaces, SIAM Journal on Control and Optimization (to appear).Google Scholar
  4. [4]
    W. H. FLEMING, R.W. RISHEL, Deterministic and Stochastic Optimal Control, Springer, Berlin, (1975).Google Scholar
  5. [5]
    L. GROSS, Potential Theory on Hilbert Space, J. Funct. Anal., 1 (1967) 123–181.Google Scholar
  6. [6]
    T. HAVÂRNEANU, Existence for the Dynamic Programming Equation of Control Diffusion Processes in Hilbert Space Nonlinear Analysis, T.M.A. (to appear).Google Scholar
  7. [7]
    P. KOTELENEZ, A Submartingale Type Inequality with Applications to Stochastic Evolution Equations, Stochastics 8 (1982) 139–151.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • G. Da Prato
    • 1
  1. 1.Scuola Normale SuperiorePisaItaly

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