Parameter identification for partially observed diffusions

Date
1992
Authors
Dabbous, T.E.
Ahmed, N.U.
Advisor
Instructor
Source Title
Journal of Optimization Theory and Applications
Print ISSN
223239
Electronic ISSN
Publisher
Kluwer Academic Publishers-Plenum Publishers
Volume
75
Issue
1
Pages
33 - 50
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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.

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Book Title
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
Citation
Published Version (Please cite this version)