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Non-Linear Filtering — The Degenerate Case

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Stochastic Differential Systems, Stochastic Control Theory and Applications

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 10))

Abstract

We consider the non-linear filtering problem where the state (or signal) satisfies

$$d{X_t} = b(t,{X_t},Y)dt + \sigma (t,{X_t},Y)d{w_t}$$
(1.1)

and the observation satisfies

$$d{Y_t} = h(t,{X_t})dt + d{\tilde w_t}$$
(1.2)

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References

  1. J.S. Baras, G.L. Blankenship, W.E. Hopkins, Existence, uniqueness and asymptotic behaviour 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. A. Bensoussan, Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam, 1982.

    MATH  Google Scholar 

  3. J.M.C. Clark, The design of robust approximations to the stochastic differential equations of non linear filtering, in Communication Systems and Random Process Theory, J. Skwirzynski ed., Sijthoff and Noordhoof (1978).

    Google Scholar 

  4. G.S. Ferreyra, The partial differential equations of non linear filtering, Ph.D dissertation, Rutgers Univ., N.J., 1983.

    Google Scholar 

  5. U.G. Haussmann, L’équation de Zakai et le problème séparé du controle optimal stochastique, in Séminaire de Probabilités XIX, Lecture Notes in Mathematics 1123, Springer Verlag, 1985.

    Google Scholar 

  6. U.G. Haussmann, The maximum principle for optimal control of diffusions with partial information, SIAM J. Control Opt., to appear 1986.

    Google Scholar 

  7. U.G. Haussmann, E. Pardoux, Time reversal of diffusions, Annals of Probability, to appear 1986.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. S.J. Sheu, Solutions of certain parabolic equations with unbounded coefficients and its application to non-linear filtering, Stochastics 10 (1983), 3146.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Department, University of British Columbia, 121 - 1984 Mathematics Road, Vancouver, B.C., V6T 1Y4, Canada

    U. G. Haussmann

Authors
  1. U. G. Haussmann
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Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island, USA

    Wendell Fleming

  2. Ceremade, Universite Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Pierre-Louis Lions

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© 1988 Springer-Verlag New York Inc.

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Haussmann, U.G. (1988). Non-Linear Filtering — The Degenerate Case. In: Fleming, W., Lions, PL. (eds) Stochastic Differential Systems, Stochastic Control Theory and Applications. The IMA Volumes in Mathematics and Its Applications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8762-6_12

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  • DOI: https://doi.org/10.1007/978-1-4613-8762-6_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8764-0

  • Online ISBN: 978-1-4613-8762-6

  • eBook Packages: Springer Book Archive

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