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      Parameter identification for partially observed diffusions

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      Author(s)
      Dabbous, T.E.
      Ahmed, N.U.
      Date
      1992
      Source Title
      Journal of Optimization Theory and Applications
      Print ISSN
      223239
      Publisher
      Kluwer Academic Publishers-Plenum Publishers
      Volume
      75
      Issue
      1
      Pages
      33 - 50
      Language
      English
      Type
      Article
      Item Usage Stats
      212
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      221
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      Abstract
      In this paper, we consider the identification problem of drift and dispersion parameters for a class of partially observed systems governed by Ito equations. Using the pathwise description of the Zakai equation, we formulate the original identification problem as a deterministic control problem in which the unnormalized conditional density (solution of the Zakai equation) is treated as the state, the unknown parameters as controls, and the likelihood ratio as the objective functional. The question of existence of elements in the parameter set that maximize the likelihood ratio is discussed. Further, using variational arguments and the Gateaux differentiability of the unnormalized density on the parameter set, we obtain the necessary conditions for optimal identification. © 1992 Plenum Publishing Corporation.
      Keywords
      distributed-parameter systems
      likelihood ratio
      Nonlinear filtering
      optimal control
      parameter identification
      Differentiation (calculus)
      Diffusion
      Distributed parameter control systems
      Mathematical models
      Optimal control systems
      Signal filtering and prediction
      State space methods
      Variational techniques
      Deterministic control problem
      Gateaux differentiability
      Ito equations
      Likelihood ratio
      Nonlinear filtering
      Optimal control
      Parameter identification
      Zakai equation
      Parameter estimation
      Permalink
      http://hdl.handle.net/11693/26100
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/BF00939904
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      • Department of Electrical and Electronics Engineering 3868
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