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Nonlinear filtering with dependent noises the case of unbounded coefficients

  • Linear and Nonlinear Filtering
  • Conference paper
  • First Online:
Analysis and Optimization of Systes

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 144))

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Abstract

This paper concerns a nonlinear filtering problem with correlated noises and a one dimensional observation process with unbounded coefficients. First, we prove the continuity of the filter with respect to the paths of the observation process. With this aim, we define a formal continuous unnormalized filter and we prove a Kallianpur-Striebel formula. Then, by means of a result given by the Malliavin calculus, we prove the existence of a regular density for the filter. Finally, we prove that the unnormalized filter is the unique solution of the Zakai equation.

URA CNRS No 399, Université de Metz INRIA LORRAINE

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Authors
  1. Patrick Florchinger
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A. Bensoussan J. L. Lions

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© 1990 Springer-Verlag

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Florchinger, P. (1990). Nonlinear filtering with dependent noises the case of unbounded coefficients. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120048

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  • DOI: https://doi.org/10.1007/BFb0120048

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52630-8

  • Online ISBN: 978-3-540-47085-4

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