Applied Mathematics and Optimization

, Volume 40, Issue 2, pp 259–272 | Cite as

Filtering with Discrete State Observations

  • F. Dufour
  • R. J. Elliott


The problem of estimating a finite state Markov chain observed via a process on the same state space is discussed. Optimal solutions are given for both the ``weak'' and ``strong'' formulations of the problem. The ``weak'' formulation proceeds using a reference probability and a measure change for the Markov chain. The ``strong'' formulation considers an observation process related to perturbations of the counting processes associated with the Markov chain. In this case the ``small noise'' convergence is investigated.

Key words. Filtering, Markov chain, Counting process, Girsanov's theorem. AMS Classification. 60J27, 93E11. 


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Copyright information

© 1999 Springer-Verlag New York Inc.

Authors and Affiliations

  • F. Dufour
    • 1
  • R. J. Elliott
    • 2
  1. 1.Laboratoire des Signaux et Systèmes, C.N.R.S. — E.S.E., Plateau de Moulon, 91192 Gif-sur-Yvette Cedex, France FR
  2. 2.Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 relliott@gpu.srv.ualberta.caCA

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