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L'equation de Zakai et le problème séparé du contrôle optimal stochastique

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Séminaire de Probabilités XIX 1983/84

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1123))

Abstract

The non-linear filtering model which arises in stochastic optimal control theory:

$$\begin{gathered}dx = f(t,x_t ,u(t,y))dt + \sigma (t,x_t ,u(t,y))dw \hfill \\dy = h(t,x_t )dt + d\hat w_t \hfill \\\end{gathered}$$

is solved and the "separated" control problem is derived under minimal regularity assumptions and minimal growth restrictions. The method relies on the robust form of the Zakai equation.

Ce travail était fait pendant que l'auteur était professeur associé au Laboratoire de Probabilité, Université de Pierre er Marie Curie, Paris, et à l'U.E.R. de Mathématiques, Université de Provence, Marseille.

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References

  1. J.S. BARAS, G.L. BLANKENSHIP et W.E. HOPKINS. Existence, uniqueness and asymptotic behavior of solutions to a class of Zakai equations with unbounded coefficients, IEEE Trans. A.C., 28(1983), 203–214.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.S. BARAS, G.L. BLANKENSHIP et S.K. MITTER. Non linear filtering of diffusion processes, Proc. IPAC Congr., Kyoto, Japan, 1981.

    Google Scholar 

  3. V.E. BENES et I. KARATZAS. On the relation of Zakai's equation and Mortensen's equation, SIAM J. Control and Optimization, 21 (1983), 472–489.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. BENSOUSSAN. Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions, Stochastics, 9 (1983), 169–222.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. BENSOUSSAN et J.L. LIONS. Applications des Inéquations Variationnelles en Contrôle Stochastique, Dunod, Paris, 1978.

    MATH  Google Scholar 

  6. G.S. FERREYRA. The robust equation of non linear filtering, preprint, Dept. of Mathematics, Louisiana State University.

    Google Scholar 

  7. W.H. FLEMING et R.W. RISHEL. Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, 1975.

    Book  MATH  Google Scholar 

  8. U.G. HAUSSMANN. Optimal control of partially observed diffusions via the separation principle, Stochastic Differential Systems, Lecture Notes in Control and Information Sciences, Vol. 43 (1982), 302–311.

    Google Scholar 

  9. G. KALLIANPUR et R.L. KARANDIKAR. A finitely additive white noise approach to nonlinear filtering, Appl.Math.Optim, 10 (1983), 159–185.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. PARDOUX. Equation du filtrage non linéaire de la prédiction et du lissage, Stochastics, 6 (1982), 193–231.

    Article  MathSciNet  MATH  Google Scholar 

  11. E. PARDOUX. Stochastic partial differential equations and filtering of diffusion processes, Stochastics, 3 (1979), 127–167.

    Article  MathSciNet  MATH  Google Scholar 

  12. S.J. SHEU. Solutions of certain parabolic equations with unbounded coefficients and its application to nonlinear filtering, Stochastics, 10 (1983), 31–46.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. STROOCK et S.R.S. VARADHAN. Multidimensional Diffusion Processes, Springer-Verlag, 1979.

    Google Scholar 

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Authors and Affiliations

  1. University of British Columbia, UK

    U. G. Haussmann

Authors
  1. U. G. Haussmann
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Jacques Azéma Marc Yor

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© 1985 Springer-Verlag

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Haussmann, U.G. (1985). L'equation de Zakai et le problème séparé du contrôle optimal stochastique. In: Azéma, J., Yor, M. (eds) Séminaire de Probabilités XIX 1983/84. Lecture Notes in Mathematics, vol 1123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075838

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  • DOI: https://doi.org/10.1007/BFb0075838

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15230-9

  • Online ISBN: 978-3-540-39397-9

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